Binary Arithmetic Implementation

Binary Arithmetic Implementation Visually

Master binary arithmetic operations with interactive visual tools and step-by-step learning

Binary Arithmetic Binary Addition Binary Subtraction Binary Multiplication Binary Division Arithmetic Logic Visual Calculation

Understanding Binary Arithmetic

Binary arithmetic is the foundation of all computer operations. Learn how computers perform mathematical calculations using only 0s and 1s.

Binary Addition

Rules:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (carry 1)

Similar to decimal addition but with base-2

Binary Subtraction

Rules:
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1 = 1 (borrow 1)

Uses borrowing from higher-order bits

Binary Multiplication

Rules:
0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1

Uses shift and add method

Binary Division

Method:
Similar to long division
Uses subtraction and shifting
Quotient and remainder

Most complex binary operation

Quick Reference

Operation Example Result
Addition 1011 + 0110 10001
Subtraction 1011 - 0110 0101
Multiplication 1011 × 0110 1000010
Division 1011 ÷ 0110 1 R 101

Decimal Equivalents

Binary Decimal

Interactive Binary Arithmetic Tools

Binary Arithmetic Calculator

Enter binary numbers and select operation:

+
-
×
÷
Operation: 1011 + 0110
Binary Result: 10001
Decimal Check: 11 + 6 = 17
Hexadecimal: B + 6 = 11

Conversion Helper

Understand the numbers you're working with:

First Operand Analysis:
Binary: 1011
Decimal: 11
Breakdown: 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8+0+2+1 = 11
Second Operand Analysis:
Binary: 0110
Decimal: 6
Breakdown: 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 0+4+2+0 = 6

Visual Binary Arithmetic

See how binary arithmetic works bit by bit:

Addition
Subtraction
Multiplication
Input Numbers:
2⁷
2⁶
2⁵
2⁴
2⁰
+

Step-by-Step Process:
Click "Animate" to see the process
Current Operation: Addition
Binary: 1011 + 0110 = 10001
Decimal: 11 + 6 = 17

Step-by-Step Binary Arithmetic

Learn the detailed process of binary arithmetic operations:

Addition
Subtraction
Multiplication
Division
Detailed Steps:
Enter numbers and select operation to begin
Current Step: 0 / 0
Progress:

Binary Arithmetic Practice

Test your skills with timed challenges:

Score: 0

Streak: 0

60

Correct: 0

Wrong: 0

Easy (4-bit)
Medium (6-bit)
Hard (8-bit)

Two's Complement Operations

Work with signed binary numbers:

Original: 1011
One's Complement: 0100
Two's Complement: 0101
Decimal Value: -5

Bitwise Operations

Perform logical operations on binary numbers:

AND
OR
XOR
NOT
Operation: 1100 AND 1010
Result: 1000
Truth Table: 1&1=1, 1&0=0, 0&1=0, 0&0=0

Shift Operations

Perform left and right bit shifts:

Original: 1011
After Shift: 10110
Decimal: 11 → 22
Effect: Multiplied by 2

Binary Converter

Convert between different number systems:

Decimal
Binary
Hex
Octal
Binary: 11111111
Decimal: 255
Hexadecimal: FF
Octal: 377