DataStructures_BinaryNumbers

Implements a binary number type in Java using array-backed storage (little-endian). Supports creation from strings or a fixed length, right shifts, addition with overflow detection, and decimal conversion. Focuses on data-structure design and explicit bit logic—no built-in integer shortcuts.

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Overview

This project models binary arithmetic at the data-structure level. It avoids Java’s native number types to highlight bitwise logic, carry propagation, and manual array manipulation.

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Features

• Create from string ("1011") or fixed length (zero-filled)
• Validate input (only '0' and '1')
• Right shift with zero fill (shiftR(int))
• Add two binaries of equal length (add(BinaryNumber)), set overflow on carry-out
• Convert to decimal (toDecimal())
• Clear overflow flag (clearOverflow())
• Robust error handling and validation

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Representation

• Endian: Little-endian (index 0 is least significant bit)
• Storage: int[] data (each entry 0 or 1)
• Overflow: Boolean flag (overflow) set when addition exceeds bit length

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Usage

Compile

# From project root (adjust path if needed)
javac -d out src/homework1/BinaryNumber.java

Quick Start (JShell or main class)

import homework1.BinaryNumber;

// Construct
BinaryNumber a = new BinaryNumber("1011"); // 11
BinaryNumber b = new BinaryNumber("0010"); // 2

// Add (same length required)
a.add(b);
System.out.println(a.toString());   // 1101
System.out.println(a.toDecimal());  // 13

// Shift right by 3 (zero-filled)
a.shiftR(3);
System.out.println(a.toString());   // 0001101

// Overflow example
BinaryNumber x = new BinaryNumber("1111");
BinaryNumber y = new BinaryNumber("0001");
x.add(y);
System.out.println(x.toString());   // Overflow
x.clearOverflow();

Note: The homework1 package implies the file path src/homework1/BinaryNumber.java.

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API Summary

Constructors

BinaryNumber(int length);     // zero-initialized
BinaryNumber(String bits);    // validates '0'/'1' only

Queries

int getLength();
int getDigit(int index);      // throws if out of range
int toDecimal();
String toString();            // returns "Overflow" if overflow flag is set

Operations

void shiftR(int amount);      // throws if amount <= 0
void add(BinaryNumber other); // throws if lengths differ
void clearOverflow();

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Error Handling

Condition	Behavior
Invalid digit string	Throws exception with clear message
Index out of bounds	getDigit() throws
Shift amount ≤ 0	shiftR() throws
Addition length mismatch	add() throws
Overflow	Flag set; call clearOverflow()

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Test Ideas

• Add two numbers with and without overflow
• Verify toDecimal() outputs expected values
• Shift by various amounts (1, length, >length)
• Ensure invalid input (like "10a1") triggers exceptions

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Notes

• Written for clarity and learning: loops and logic are explicit rather than optimized.