773 lines
		
	
	
	
		
			21 KiB
		
	
	
	
		
			Markdown
		
	
	
	
	
	
			
		
		
	
	
			773 lines
		
	
	
	
		
			21 KiB
		
	
	
	
		
			Markdown
		
	
	
	
	
	
# Multi-Base Calculator System
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## Technical Manual and Documentation
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**Document Version:** 1.0
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**Publication Date:** October 24, 2025
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**Target Platform:** NXP LPC1768 ARM Cortex-M3 Microcontroller
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**Document Status:** Final Release
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---
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## Table of Contents
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1. [System Overview](#1-system-overview)
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2. [Hardware Architecture](#2-hardware-architecture)
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3. [Pin Configuration](#3-pin-configuration)
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4. [Software Architecture](#4-software-architecture)
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5. [Functional Specification](#5-functional-specification)
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6. [Code Documentation](#6-code-documentation)
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7. [Operating Procedures](#7-operating-procedures)
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8. [Technical Reference](#8-technical-reference)
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---
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## 1. System Overview
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### 1.1 Executive Summary
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This document describes a multi-base arithmetic calculator implemented on the LPC1768 ARM Cortex-M3 microcontroller. The system performs calculations in Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16) number systems.
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### 1.2 System Features
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- Four numerical base modes with dynamic switching
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- 4×4 matrix keypad for input
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- 16×2 LCD display for status and results
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- Single-digit 7-segment display for quick reference
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- Three arithmetic operations: Addition, Subtraction, Multiplication
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- Shift-key operator access mechanism
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- Hardware debouncing for stable input
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### 1.3 System Architecture
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```
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┌──────────────────────────────────────────┐
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│         LPC1768 Microcontroller          │
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│            (ARM Cortex-M3)               │
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├──────────┬──────────────┬────────────────┤
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│          │              │                │
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│  Input   │  Processing  │    Output      │
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│ Keypad   │  Calculator  │  LCD Display   │
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│  (4×4)   │    Logic     │  7-Segment     │
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│  Button  │   Base Conv. │                │
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└──────────┴──────────────┴────────────────┘
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```
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### 1.4 Operating Modes
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| Mode | Base | Valid Digits | Application |
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|------|------|--------------|-------------|
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| DEC | 10 | 0-9 | General arithmetic |
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| BIN | 2 | 0-1 | Digital logic |
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| OCT | 8 | 0-7 | Unix permissions |
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| HEX | 16 | 0-9, A-F | Memory addressing |
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---
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## 2. Hardware Architecture
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### 2.1 Component Specifications
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**Microcontroller (LPC1768):**
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- ARM Cortex-M3 core, 100 MHz
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- 512 KB Flash, 32 KB SRAM
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- 70 GPIO pins (5V tolerant)
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- 3.3V operating voltage
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**Input Subsystem:**
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- 4×4 matrix keypad (16 keys)
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- Mode selection button (P2.12)
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- Software debouncing (9ms effective)
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**Output Subsystem:**
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- 16×2 LCD (HD44780-compatible, 4-bit mode)
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- 7-segment LED display (single digit)
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- Real-time display updates
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### 2.2 System Block Diagram
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```
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Input Processing          Calculator Core         Output System
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┌────────────┐           ┌──────────────┐        ┌──────────────┐
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│  Keypad    │──────────>│ State        │───────>│ LCD Display  │
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│  Scanning  │           │ Machine      │        │ (16×2)       │
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│            │           │              │        │              │
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│  Mode      │──────────>│ Arithmetic   │───────>│ 7-Segment    │
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│  Button    │           │ Engine       │        │ (Single)     │
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│            │           │              │        │              │
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│  Debounce  │           │ Base         │        │ Feedback     │
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│  Logic     │           │ Conversion   │        │ Messages     │
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└────────────┘           └──────────────┘        └──────────────┘
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```
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---
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## 3. Pin Configuration
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### 3.1 Connector Overview
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The LPC1768 board provides four 10-pin FRC connectors (CNA, CNB, CNC, CND) for peripheral interfacing.
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### 3.2 Connector CNA - 7-Segment Display
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**Function:** Seven-segment LED display driver (P0.4-P0.11)
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| Pin | LPC1768 | Port.Bit | Function | Direction |
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|-----|---------|----------|----------|-----------|
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| 1 | 81 | P0.4 | Segment A | Output |
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| 2 | 80 | P0.5 | Segment B | Output |
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| 3 | 79 | P0.6 | Segment C | Output |
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| 4 | 78 | P0.7 | Segment D | Output |
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| 5 | 77 | P0.8 | Segment E | Output |
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| 6 | 76 | P0.9 | Segment F | Output |
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| 7 | 48 | P0.10 | Segment G | Output |
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| 8 | 49 | P0.11 | Decimal Point | Output |
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| 10 | - | GND | Ground | - |
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**7-Segment Encoding Array:**
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```c
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const unsigned char seven_seg[16] = {
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    0x3F, 0x06, 0x5B, 0x4F,  // 0-3
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    0x66, 0x6D, 0x7D, 0x07,  // 4-7
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    0x7F, 0x6F, 0x77, 0x7C,  // 8-B
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    0x39, 0x5E, 0x79, 0x71   // C-F
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};
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```
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### 3.3 Connector CNB - Display Enable and Mode Button
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**Function:** 7-segment enable and mode selection (P1.23, P2.12)
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| Pin | LPC1768 | Port.Bit | Function | Direction |
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|-----|---------|----------|----------|-----------|
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| 1 | 37 | P1.23 | 7-Seg Digit Enable | Output |
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| 7 | 51 | P2.12 | Mode Button | Input (Pull-up) |
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| 10 | - | GND | Ground | - |
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### 3.4 Connector CNC - Keypad Matrix
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**Function:** 4×4 keypad interface (P0.15-P0.22)
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| Pin | LPC1768 | Port.Bit | Function | Direction |
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|-----|---------|----------|----------|-----------|
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| 1 | 62 | P0.15 | Column 0 | Output |
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| 2 | 63 | P0.16 | Column 1 | Output |
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| 3 | 61 | P0.17 | Column 2 | Output |
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| 4 | 60 | P0.18 | Column 3 | Output |
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| 5 | 59 | P0.19 | Row 0 | Input (Pull-up) |
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| 6 | 58 | P0.20 | Row 1 | Input (Pull-up) |
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| 7 | 57 | P0.21 | Row 2 | Input (Pull-up) |
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| 8 | 56 | P0.22 | Row 3 | Input (Pull-up) |
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| 10 | - | GND | Ground | - |
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**Keypad Layout:**
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```
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     Col0   Col1   Col2   Col3
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      │      │      │      │
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Row0──┼──0───┼──1───┼──2───┼──3──
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Row1──┼──4───┼──5───┼──6───┼──7──
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Row2──┼──8───┼──9───┼──A───┼──B──
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Row3──┼──C───┼──D───┼──E───┼──F──
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```
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**Key Index Calculation:** `Key = (Column × 4) + Row`
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### 3.5 Connector CND - LCD Display
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**Function:** HD44780 LCD interface in 4-bit mode (P0.23-P0.28)
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| Pin | LPC1768 | Port.Bit | Function | Direction |
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|-----|---------|----------|----------|-----------|
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| 1 | 9 | P0.23 | LCD D4 | Output |
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| 2 | 8 | P0.24 | LCD D5 | Output |
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| 3 | 7 | P0.25 | LCD D6 | Output |
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| 4 | 6 | P0.26 | LCD D7 | Output |
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| 5 | 25 | P0.27 | LCD RS | Output |
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| 6 | 24 | P0.28 | LCD EN | Output |
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| 10 | - | GND | Ground | - |
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**LCD Control Signals:**
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- **RS (Register Select):** 0 = Command, 1 = Data
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- **EN (Enable):** Falling edge latches data
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- **D4-D7:** 4-bit data interface
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### 3.6 Pin Mapping Summary
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| Function | Pins | Connector | Direction | Count |
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|----------|------|-----------|-----------|-------|
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| 7-Segment Data | P0.4-P0.11 | CNA | Output | 8 |
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| Keypad Columns | P0.15-P0.18 | CNC | Output | 4 |
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| Keypad Rows | P0.19-P0.22 | CNC | Input | 4 |
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| LCD Data | P0.23-P0.26 | CND | Output | 4 |
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| LCD Control | P0.27-P0.28 | CND | Output | 2 |
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| 7-Seg Enable | P1.23 | CNB | Output | 1 |
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| Mode Button | P2.12 | CNB | Input | 1 |
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| **Total** | - | - | - | **24** |
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---
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## 4. Software Architecture
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### 4.1 System Design Overview
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The software follows a polled input, state-based architecture with three primary layers:
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1. **Application Layer:** User interface and calculator logic
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2. **Hardware Abstraction:** LCD, keypad, and display control functions
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3. **Hardware Access:** Direct register manipulation
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### 4.2 State Machine
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```
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┌──────────┐
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│   INIT   │
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└─────┬────┘
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      │
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      ▼
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┌──────────┐     ┌─────────────┐
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│   IDLE   │────>│ DIGIT INPUT │
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│  READY   │     └──────┬──────┘
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└─────┬────┘            │
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      │                 ▼
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      │           ┌──────────────┐
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      │           │ ACCUMULATE   │
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      │           │   NUMBER     │
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      │           └──────┬───────┘
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      │                  │
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      ├──────────────────┤
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      │                  │
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      ▼                  ▼
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┌──────────┐      ┌──────────────┐
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│  SHIFT   │────> │  OPERATOR    │
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│  DETECT  │      │   PENDING    │
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└──────────┘      └──────┬───────┘
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      │                  │
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      ▼                  ▼
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┌──────────┐      ┌──────────────┐
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│   MODE   │      │  CALCULATE   │
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│  CHANGE  │      │   RESULT     │
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└──────────┘      └──────────────┘
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```
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### 4.3 Global State Variables
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```c
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// Calculator state
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unsigned int current_base;     // Active base (2, 8, 10, 16)
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unsigned int input_num;        // Current input number
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unsigned int stored_num;       // First operand
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unsigned int operation;        // Pending operation (0-3)
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unsigned int result;           // Calculation result
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// Input state
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unsigned int key, last_key;    // Key scan results
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unsigned int stable;           // Debounce counter
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unsigned int shift_active;     // Shift key flag
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// Mode button state
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unsigned int button_state, last_button_state;
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unsigned int button_stable;    // Button debounce counter
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```
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### 4.4 Constant Definitions
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```c
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// Operational modes
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#define MODE_BIN  2
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#define MODE_OCT  8
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#define MODE_DEC  10
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#define MODE_HEX  16
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// Operations
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#define OP_NONE  0
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#define OP_ADD   1
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#define OP_SUB   2
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#define OP_MUL   3
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// Hardware pins
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#define COL_BASE 15
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#define ROW_BASE 19
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#define COL_MASK (0x0F << COL_BASE)
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#define ROW_MASK (0x0F << ROW_BASE)
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#define SEG_SHIFT 4
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#define DIGIT_EN (1<<23)
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#define LCD_DATA_SHIFT 23
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#define LCD_DATA_MASK (0x0F << LCD_DATA_SHIFT)
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#define LCD_RS (1<<27)
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#define LCD_EN (1<<28)
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#define MODE_BUTTON (1<<12)
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```
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### 4.5 Main Program Flow
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```c
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int main(void){
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    // Initialize hardware
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    configure_pins();
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    configure_gpio();
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    lcd_init();
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    // Initial display
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    display_mode();
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    display_input();
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    // Main loop
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    for(;;){
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        // Input acquisition
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        shift_active = is_key0_pressed();
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        key = scan_keypad();
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        button_state = scan_mode_button();
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        // Debouncing
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        debounce_keypad();
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        debounce_button();
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        // Mode change
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        if(stable_mode_press()){
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            cycle_mode();
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        }
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        // Key processing
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        if(stable_key_press()){
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            if(shift_active){
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                process_operator(key);
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            } else {
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                process_digit(key);
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            }
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        }
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        // Display update
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        update_7segment();
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        delay(3000);  // 3ms scan interval
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    }
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}
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```
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---
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## 5. Functional Specification
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### 5.1 Numerical Base Modes
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| Mode | Base | Valid Keys | Input Example | Display |
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|------|------|------------|---------------|---------|
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| DEC | 10 | 0-9 | 123 | "123" |
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| BIN | 2 | 0-1 | 1011 | "1011" |
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| OCT | 8 | 0-7 | 177 | "177" |
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| HEX | 16 | 0-9, A-F | 1A2F | "1A2F" |
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**Input Accumulation Algorithm:**
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```c
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// For any base:
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input_num = input_num * current_base + key_value;
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// Example (HEX): A, B → AB
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// Step 1: 0 * 16 + 10 = 10
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// Step 2: 10 * 16 + 11 = 171 (0xAB)
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```
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### 5.2 Operator Functions
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**Shift Key Paradigm:** Key 0 acts as a modifier for operator access.
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| Key Combo | Function | Operation | Display |
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|-----------|----------|-----------|---------|
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| 0 + B | Addition | stored + input | "Op: +" |
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| 0 + C | Clear | Reset all | "Op: CLR" |
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| 0 + D | Subtraction | stored - input | "Op: -" |
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| 0 + E | Multiplication | stored × input | "Op: *" |
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| 0 + F | Equals | Calculate result | "Res: XXX" |
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**Operation Sequence:**
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```
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1. Enter first number
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2. Hold Key 0 + Press operator (B/D/E)
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3. Enter second number
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4. Hold Key 0 + Press F (equals)
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5. View result on LCD
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```
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### 5.3 Input Processing
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**Debouncing:** Key must be stable for 3 consecutive scans (9ms total).
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```c
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if(key == last_key){
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    if(stable < 5) stable++;
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} else {
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    last_key = key;
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    stable = 0;
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}
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if(stable == 3 && key != 0xFF){
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    process_key(key);
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    stable = 5;  // Lock-out
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}
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```
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**Digit Validation:**
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```c
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unsigned int is_valid_digit(unsigned int key){
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    if(key >= 16) return 0;
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    if(current_base == MODE_BIN && key >= 2) return 0;
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    if(current_base == MODE_OCT && key >= 8) return 0;
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    if(current_base == MODE_DEC && key >= 10) return 0;
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    return 1;  // Valid in HEX
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}
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```
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---
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## 6. Code Documentation
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### 6.1 Peripheral Control Functions
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#### Keypad Scanning
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```c
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unsigned int scan_keypad(void){
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    unsigned int col, row, row_bits;
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    for(col = 0; col < 4; col++){
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        LPC_GPIO0->FIOSET = COL_MASK;         // All columns HIGH
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        delay(50);
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        LPC_GPIO0->FIOCLR = (1 << (COL_BASE + col));  // Pull column LOW
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        delay(200);
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        row_bits = (LPC_GPIO0->FIOPIN & ROW_MASK) >> ROW_BASE;
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        if(row_bits != 0x0F){  // Key detected
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            for(row = 0; row < 4; row++){
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                if((row_bits & (1 << row)) == 0){
 | 
						||
                    LPC_GPIO0->FIOSET = COL_MASK;
 | 
						||
                    return (col * 4) + row;
 | 
						||
                }
 | 
						||
            }
 | 
						||
        }
 | 
						||
    }
 | 
						||
 | 
						||
    LPC_GPIO0->FIOSET = COL_MASK;
 | 
						||
    return 0xFF;  // No key pressed
 | 
						||
}
 | 
						||
```
 | 
						||
 | 
						||
#### Shift Key Detection
 | 
						||
 | 
						||
```c
 | 
						||
unsigned int is_key0_pressed(void){
 | 
						||
    unsigned int row_bits;
 | 
						||
 | 
						||
    // Check Key 0 (Column 0, Row 0)
 | 
						||
    LPC_GPIO0->FIOSET = COL_MASK;
 | 
						||
    delay(50);
 | 
						||
    LPC_GPIO0->FIOCLR = (1 << COL_BASE);
 | 
						||
    delay(200);
 | 
						||
    row_bits = (LPC_GPIO0->FIOPIN & ROW_MASK) >> ROW_BASE;
 | 
						||
    LPC_GPIO0->FIOSET = COL_MASK;
 | 
						||
 | 
						||
    return ((row_bits & 0x01) == 0) ? 1 : 0;
 | 
						||
}
 | 
						||
```
 | 
						||
 | 
						||
### 6.2 LCD Control Functions
 | 
						||
 | 
						||
#### LCD Initialization (4-bit Mode)
 | 
						||
 | 
						||
```c
 | 
						||
void lcd_init(void){
 | 
						||
    lcd_delay(5000000);  // Power-on wait
 | 
						||
 | 
						||
    // 8-bit mode initialization
 | 
						||
    lcd_write_nibble(0x03, 0);
 | 
						||
    lcd_delay(500000);
 | 
						||
    lcd_write_nibble(0x03, 0);
 | 
						||
    lcd_delay(500000);
 | 
						||
    lcd_write_nibble(0x03, 0);
 | 
						||
    lcd_delay(500000);
 | 
						||
 | 
						||
    // Switch to 4-bit mode
 | 
						||
    lcd_write_nibble(0x02, 0);
 | 
						||
    lcd_delay(500000);
 | 
						||
 | 
						||
    lcd_cmd(0x28);  // 4-bit, 2 lines, 5x8 font
 | 
						||
    lcd_cmd(0x0C);  // Display ON, cursor OFF
 | 
						||
    lcd_cmd(0x01);  // Clear display
 | 
						||
    lcd_delay(500000);
 | 
						||
    lcd_cmd(0x06);  // Entry mode: increment
 | 
						||
}
 | 
						||
```
 | 
						||
 | 
						||
#### LCD Communication
 | 
						||
 | 
						||
```c
 | 
						||
void lcd_write_nibble(unsigned char nibble, unsigned char is_data){
 | 
						||
    unsigned long temp;
 | 
						||
    temp = (nibble & 0x0F) << LCD_DATA_SHIFT;
 | 
						||
    LPC_GPIO0->FIOPIN = (LPC_GPIO0->FIOPIN & ~LCD_DATA_MASK) | temp;
 | 
						||
 | 
						||
    if(is_data)
 | 
						||
        LPC_GPIO0->FIOSET = LCD_RS;  // Data mode
 | 
						||
    else
 | 
						||
        LPC_GPIO0->FIOCLR = LCD_RS;  // Command mode
 | 
						||
 | 
						||
    LPC_GPIO0->FIOSET = LCD_EN;      // EN pulse
 | 
						||
    lcd_delay(100);
 | 
						||
    LPC_GPIO0->FIOCLR = LCD_EN;
 | 
						||
    lcd_delay(500000);
 | 
						||
}
 | 
						||
 | 
						||
void lcd_cmd(unsigned char cmd){
 | 
						||
    lcd_write_nibble(cmd >> 4, 0);     // High nibble
 | 
						||
    lcd_write_nibble(cmd & 0x0F, 0);   // Low nibble
 | 
						||
}
 | 
						||
 | 
						||
void lcd_data(unsigned char data){
 | 
						||
    lcd_write_nibble(data >> 4, 1);    // High nibble
 | 
						||
    lcd_write_nibble(data & 0x0F, 1);  // Low nibble
 | 
						||
}
 | 
						||
```
 | 
						||
 | 
						||
### 6.3 Display Functions
 | 
						||
 | 
						||
#### Number Display (Base Conversion)
 | 
						||
 | 
						||
```c
 | 
						||
void lcd_print_num(unsigned int num, unsigned int base){
 | 
						||
    char buffer[17];
 | 
						||
    int i = 0;
 | 
						||
 | 
						||
    if(num == 0){
 | 
						||
        lcd_data('0');
 | 
						||
        return;
 | 
						||
    }
 | 
						||
 | 
						||
    // Extract digits in reverse
 | 
						||
    while(num > 0 && i < 16){
 | 
						||
        unsigned int digit = num % base;
 | 
						||
        if(digit < 10)
 | 
						||
            buffer[i++] = '0' + digit;
 | 
						||
        else
 | 
						||
            buffer[i++] = 'A' + (digit - 10);
 | 
						||
        num = num / base;
 | 
						||
    }
 | 
						||
 | 
						||
    // Print in correct order
 | 
						||
    while(i > 0){
 | 
						||
        lcd_data(buffer[--i]);
 | 
						||
    }
 | 
						||
}
 | 
						||
```
 | 
						||
 | 
						||
#### Mode Display
 | 
						||
 | 
						||
```c
 | 
						||
void display_mode(void){
 | 
						||
    lcd_cmd(0x80);  // Line 1
 | 
						||
    lcd_print_str("Mode: ");
 | 
						||
 | 
						||
    if(current_base == MODE_BIN)
 | 
						||
        lcd_print_str("BIN     ");
 | 
						||
    else if(current_base == MODE_OCT)
 | 
						||
        lcd_print_str("OCT     ");
 | 
						||
    else if(current_base == MODE_DEC)
 | 
						||
        lcd_print_str("DEC     ");
 | 
						||
    else
 | 
						||
        lcd_print_str("HEX     ");
 | 
						||
}
 | 
						||
```
 | 
						||
 | 
						||
### 6.4 GPIO Configuration
 | 
						||
 | 
						||
```c
 | 
						||
void configure_system(void){
 | 
						||
    // Pin function selection (GPIO mode)
 | 
						||
    LPC_PINCON->PINSEL0 = 0;
 | 
						||
    LPC_PINCON->PINSEL1 = 0;
 | 
						||
    LPC_PINCON->PINSEL3 = 0;
 | 
						||
    LPC_PINCON->PINSEL4 = 0;
 | 
						||
 | 
						||
    // GPIO direction setup
 | 
						||
    LPC_GPIO0->FIODIR |= COL_MASK;            // Columns: output
 | 
						||
    LPC_GPIO0->FIODIR &= ~ROW_MASK;           // Rows: input
 | 
						||
    LPC_GPIO0->FIODIR |= (0xFF << SEG_SHIFT); // Segments: output
 | 
						||
    LPC_GPIO0->FIODIR |= LCD_DATA_MASK | LCD_RS | LCD_EN;
 | 
						||
    LPC_GPIO1->FIODIR |= DIGIT_EN;
 | 
						||
    LPC_GPIO2->FIODIR &= ~MODE_BUTTON;
 | 
						||
 | 
						||
    // Initial states
 | 
						||
    LPC_GPIO0->FIOSET = COL_MASK;  // Columns inactive
 | 
						||
}
 | 
						||
```
 | 
						||
 | 
						||
---
 | 
						||
 | 
						||
## 7. Operating Procedures
 | 
						||
 | 
						||
### 7.1 Basic Operation
 | 
						||
 | 
						||
**Power-On Sequence:**
 | 
						||
1. System initializes, LCD displays: "Mode: DEC" / "Inp: 0"
 | 
						||
2. Select base using P2.12 button (DEC → BIN → OCT → HEX → DEC)
 | 
						||
3. Begin entering numbers
 | 
						||
 | 
						||
**Numeric Input:**
 | 
						||
- Press digit keys (0-9, A-F as valid for current base)
 | 
						||
- LCD shows accumulated number: "Inp: XXX"
 | 
						||
- 7-segment displays last hexadecimal digit
 | 
						||
 | 
						||
**Arithmetic Operations:**
 | 
						||
1. Enter first number
 | 
						||
2. Hold Key 0, press operator key (B/D/E)
 | 
						||
3. LCD shows: "Op: +/-/*"
 | 
						||
4. Enter second number
 | 
						||
5. Hold Key 0, press F (equals)
 | 
						||
6. LCD shows: "Res: XXX"
 | 
						||
 | 
						||
**Clear Function:**
 | 
						||
- Hold Key 0, press C
 | 
						||
- All values reset to zero
 | 
						||
- Current mode preserved
 | 
						||
 | 
						||
### 7.2 Usage Examples
 | 
						||
 | 
						||
**Example 1: Decimal Addition (25 + 17)**
 | 
						||
```
 | 
						||
1. Mode: DEC
 | 
						||
2. Press 2, 5 → "Inp: 25"
 | 
						||
3. Hold 0 + B → "Op: +"
 | 
						||
4. Press 1, 7 → "Inp: 17"
 | 
						||
5. Hold 0 + F → "Res: 42"
 | 
						||
```
 | 
						||
 | 
						||
**Example 2: Hexadecimal Calculation (AB + 1F)**
 | 
						||
```
 | 
						||
1. Press P2.12 until "Mode: HEX"
 | 
						||
2. Press A, B → "Inp: AB"
 | 
						||
3. Hold 0 + B → "Op: +"
 | 
						||
4. Press 1, F → "Inp: 1F"
 | 
						||
5. Hold 0 + F → "Res: CA"
 | 
						||
```
 | 
						||
 | 
						||
**Example 3: Binary Multiplication (101 × 11)**
 | 
						||
```
 | 
						||
1. Select "Mode: BIN"
 | 
						||
2. Press 1, 0, 1 → "Inp: 101"
 | 
						||
3. Hold 0 + E → "Op: *"
 | 
						||
4. Press 1, 1 → "Inp: 11"
 | 
						||
5. Hold 0 + F → "Res: 1111"
 | 
						||
```
 | 
						||
 | 
						||
### 7.3 Key Reference
 | 
						||
 | 
						||
**Numeric Input:**
 | 
						||
- Keys 0-9: Decimal digits (base-dependent)
 | 
						||
- Keys A-F: Hexadecimal digits (HEX mode only)
 | 
						||
 | 
						||
**Operators (Hold Key 0 + Press):**
 | 
						||
- Key B: Addition (+)
 | 
						||
- Key C: Clear (CLR)
 | 
						||
- Key D: Subtraction (-)
 | 
						||
- Key E: Multiplication (×)
 | 
						||
- Key F: Equals (=)
 | 
						||
 | 
						||
**Mode Control:**
 | 
						||
- P2.12 Button: Cycle through bases
 | 
						||
 | 
						||
### 7.4 System Limitations
 | 
						||
 | 
						||
| Parameter | Limit | Notes |
 | 
						||
|-----------|-------|-------|
 | 
						||
| Maximum Input | 65535 | 16-bit unsigned integer |
 | 
						||
| Display Digits | Variable | Based on current base |
 | 
						||
| Overflow Behavior | Wrap-around | Result % 65536 |
 | 
						||
| Underflow Behavior | Wrap-around | Unsigned arithmetic |
 | 
						||
| Operations | 3 | Add, Subtract, Multiply |
 | 
						||
| Decimal Support | No | Integer only |
 | 
						||
 | 
						||
---
 | 
						||
 | 
						||
## 8. Technical Reference
 | 
						||
 | 
						||
### 8.1 LCD Command Set
 | 
						||
 | 
						||
| Command | Code | Function |
 | 
						||
|---------|------|----------|
 | 
						||
| Clear Display | 0x01 | Clear all, cursor home |
 | 
						||
| Return Home | 0x02 | Cursor to position 0 |
 | 
						||
| Entry Mode | 0x06 | Increment, no shift |
 | 
						||
| Display Control | 0x0C | Display ON, cursor OFF |
 | 
						||
| Function Set | 0x28 | 4-bit, 2 lines, 5×8 |
 | 
						||
| Set Line 1 | 0x80 | Cursor to line 1 |
 | 
						||
| Set Line 2 | 0xC0 | Cursor to line 2 |
 | 
						||
 | 
						||
### 8.2 Timing Specifications
 | 
						||
 | 
						||
| Parameter | Value | Unit |
 | 
						||
|-----------|-------|------|
 | 
						||
| Keypad Scan Interval | 3 | ms |
 | 
						||
| Debounce Time | 9 | ms |
 | 
						||
| LCD Enable Pulse | 100 | μs |
 | 
						||
| LCD Processing Delay | 500 | ms (software) |
 | 
						||
| 7-Segment Update | Real-time | - |
 | 
						||
 | 
						||
### 8.3 Memory Usage
 | 
						||
 | 
						||
| Component | Size |
 | 
						||
|-----------|------|
 | 
						||
| Program Code | ~4 KB |
 | 
						||
| Global Variables | 48 bytes |
 | 
						||
| Stack Usage | ~512 bytes |
 | 
						||
| LCD Buffer | None (direct write) |
 | 
						||
 | 
						||
### 8.4 Power Consumption
 | 
						||
 | 
						||
| Component | Typical | Maximum |
 | 
						||
|-----------|---------|---------|
 | 
						||
| LPC1768 MCU | 50 mA | 100 mA |
 | 
						||
| LCD Display | 2 mA | 5 mA |
 | 
						||
| LCD Backlight | 20 mA | 50 mA |
 | 
						||
| 7-Segment | 10 mA | 80 mA |
 | 
						||
| Total System | 82 mA | 235 mA |
 | 
						||
 | 
						||
### 8.5 Error Handling
 | 
						||
 | 
						||
**Invalid Input:** Silently ignored (no response)
 | 
						||
 | 
						||
**Overflow:** Modulo arithmetic applied
 | 
						||
```c
 | 
						||
if(input_num > 65535)
 | 
						||
    input_num = input_num % 65536;
 | 
						||
```
 | 
						||
 | 
						||
**Underflow:** Unsigned wrap-around
 | 
						||
```c
 | 
						||
// Example: 5 - 10 = 65531 (not -5)
 | 
						||
```
 | 
						||
 | 
						||
---
 | 
						||
 | 
						||
## Appendices
 | 
						||
 | 
						||
### A. Complete Code Listing
 | 
						||
 | 
						||
The complete source code is provided in the implementation section of this document.
 | 
						||
 | 
						||
### B. Troubleshooting Guide
 | 
						||
 | 
						||
| Issue | Cause | Solution |
 | 
						||
|-------|-------|----------|
 | 
						||
| No keypad response | GPIO configuration | Verify COL_MASK and ROW_MASK |
 | 
						||
| LCD blank | Initialization failure | Check timing delays |
 | 
						||
| Incorrect display | Base mismatch | Verify current_base value |
 | 
						||
| Mode button stuck | Debounce too short | Increase button_stable threshold |
 | 
						||
 | 
						||
### C. Revision History
 | 
						||
 | 
						||
| Version | Date | Changes |
 | 
						||
|---------|------|---------|
 | 
						||
| 1.0 | 2025-10-24 | Initial release |
 |