Four-Function Calculator

EE4953 Project | Fall 2022
GitHub Repository

Team Members

• Dominic Benintendi – Parser/Lexer development, system architecture
• Devin Macy – LCD/keypad logic, input handling, shift/button mappings
• Colin Russell – Documentation, user guide, interface design
• AL-Husain Bani Oraba – Diagrams, system requirements, documentation support

Overview

I designed and built a fully functional four-function calculator using an Arduino Nano, 1602 LCD, and a 4x4 membrane keypad. The goal was to create a reliable and user-friendly device that adheres to the standard conventions of modern calculators while operating within hardware constraints.

Features

• Arithmetic: Add, subtract, multiply, divide
• Extra operations: Parentheses, exponents, floating point
• Syntax error handling with helpful messages
• Expression editing with arrow keys, insert/delete
• History navigation for past expressions
• Dual clear functionality: Clear and Clear All

Hardware

• Microcontroller: Arduino Nano
  

  

• Display: 1602 LCD via I2C
  

  

• Input: 4x4 membrane keypad + 2 shift pushbuttons
  

  

• Power: 5V via USB Mini-B

Keypad Mapping

• Mode Switching: Due to the limited number of keys on the keypad, mode switching was used
• Default Mode: A–D → + - * /, adjacent key → =, lower left → Clear

  

• Left Shift Mode (L): Arrow keys, del, ins

  

• Right Shift Mode (R): (), ., ^, Clear All

  

Software

• Input parsing: Lexer/tokenizer and recursive descent parser
• Computation: Infix notation with proper order of operations
• Display logic: Shows expressions and results with context-aware alignment
• Error handling: Returns messages like ERR:SYNTAX, ERR:DIV BY 0, etc.

System Design

• Modules:

  • CalcLexer – Tokenizes user input
  • CalcParser – Recursively evaluates expressions
  • LcdController – Manages LCD content
  • KeypadController – Maps key inputs and shift states

• Architecture: Clean object-oriented design with clearly divided subsystems for input, display, and computation.

Build Diagrams

• TinkerCAD schematic of the system
• Breadboard and wiring layouts
• LCD and keypad pin connections
• Flowcharts for data processing and system interaction

Operating Notes

• Operates in 40%±30% humidity and –40°F to 185°F
• Not resistant to drops or moisture—no protective chassis
• Powered exclusively via USB

Expression Evaluation: Lexer & Parser

To support full arithmetic expressions (including parentheses, exponents, and floating-point numbers), we developed a custom recursive descent parser backed by a lexer/tokenizer. This allowed us to move beyond simple two-number operations and handle full algebraic expressions with correct operator precedence and error detection.

🔍 Lexer (Tokenizer)

The lexer scans the raw input string and converts it into a stream of tokens. These tokens represent numbers, operators (+, -, *, /, ^), parentheses, and the end of the expression.

Token types included:

• NUM: Any numeric value (integer or float)
• ADD, SUB, MUL, DIV, POW: Arithmetic operators
• L_PAR, R_PAR: Left and right parentheses
• END: End of expression

Example:

Input: "5 / (6 + 2)"
Tokens: NUM DIV L_PAR NUM ADD NUM R_PAR

🧠 Parser (Recursive Descent)

The parser evaluates the token stream using a context-free grammar with recursion to respect the order of operations:

Operand:
  → **NUM**

EXP:
  → Operand
  | **LEFT_PAR** ADD_SUB_EXP **RIGHT_PAR**
  | **SUB** ADD_SUB_EXP

POW_EXP:
  → EXP **POW** EXP
  | EXP

MUL_DIV_EXP:
  → POW_EXP **MUL** POW_EXP
  | POW_EXP **DIV** POW_EXP
  | POW_EXP

ADD_SUB_EXP:
  → MUL_DIV_EXP **ADD** MUL_DIV_EXP
  | MUL_DIV_EXP **SUB** MUL_DIV_EXP
  | MUL_DIV_EXP

This approach supports:

• Proper precedence: * and / before + and -, and ^ before both
• Associativity: Left-to-right for most ops, right-to-left for ^
• Parentheses for grouping
• Negative numbers and unary minus (e.g., -5, 2 + -6)
• Floating point precision with 2-decimal accuracy on LCD

🛠 Error Handling

The lexer/parser combination detects and reports:

• ERR:SYNTAX – Invalid token arrangement
• ERR:DIV BY 0 – Division by zero
• ERR:DECM SYNTAX – Multiple decimal points in a number
• ERR:NO R_PAR – Missing closing parenthesis

🧪 Sample Evaluations

Input: 5 + 3 * 5 → Output: 20 (Multiplication before addition) 

Input: (5 + 3) * 5 → Output: 40 (Parentheses override precedence)

Input: 5 * ((4 - 5)/0.5) → Output: -10 (Nested expressions + float division)

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