Binary Calculator
Perform binary arithmetic, bitwise logic operations, and convert values across binary, decimal, hex, and octal numbering systems.
= 10 (decimal) = 0xA (hex)
= 6 (decimal) = 0x6 (hex)
Result
10000
= 16 (decimal) = 0x10 (hex)
Number Base Converter
How to Use the Binary Calculator
- Enter valid binary numbers (composed of 0 and 1) into the input fields.
- Choose an arithmetic operation (+, -, ×) or bitwise operation (AND, OR, XOR).
- View the instant output in binary alongside equivalent decimal, hexadecimal, and octal representations.
Formulas & Principles
Binary Addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (0 carry 1)
Binary Subtraction: 0-0=0, 1-0=1, 1-1=0, 10-1=1 (borrow 1)
Bitwise AND: 1 only if both bits are 1
Bitwise OR: 1 if at least one bit is 1
Bitwise XOR: 1 if bits are different (0^1=1, 1^0=1)
Frequently Asked Questions
How do you convert binary to decimal manually?
Multiply each binary digit by 2 raised to the power of its position index (starting with 0 from the rightmost digit) and sum all the products together.
What is two's complement representation?
Two's complement is a mathematical technique used in computer systems to represent signed negative integers by inverting all bits (one's complement) and adding 1.
Why is binary arithmetic fundamental in computing?
Modern microprocessors and digital logic gates operate with two voltage states (on/off, high/low), making binary base-2 representation the foundation of all computing hardware.
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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