Binary Calculator

The Binary Calculator performs arithmetic and bitwise operations on binary (base 2) numbers. Binary is the fundamental number system used by computers, built from only two digits: 0 and 1. Each position represents a power of 2, which is why a simple string of bits can encode any number.

Why base 2? Digital circuits have two stable states — off and on — so every value inside a computer is ultimately stored as binary. This tool lets you compute on those values directly, without converting by hand.

Common Use Cases

Low-Level Programming

Test bit masks, flags, and shift logic before writing them into firmware, drivers, or embedded code.

Learning & Homework

Check binary addition and bitwise exercises for computer science and digital logic courses.

Networking & Masks

Work out subnet masks and bit-level flags where AND and OR define how addresses are split.

How to Use the Binary Calculator

Enter the First Number

Type the first binary number using only the digits 0 and 1. The 0b prefix is added automatically, so you only enter the bits themselves.

Choose an Operator

Pick an arithmetic operator (+, −, ×, ÷, %) or a bitwise operator (&, |, ^, «, »). Bitwise operators are available on the Binary tab.

Enter the Second Number

Type the second binary value into the lower field. For shift operations this is the number of positions to shift.

Calculate & Read Results

Click Calculate or press Enter. The result appears in binary, octal, decimal, and hexadecimal at once, each with a one-click copy button.

Quick start: Use the Try examples chips to load a ready-made expression, then tweak the values to explore how the result changes across all four bases.

Features

Arithmetic & Bitwise Operations

Every operator the calculator supports is listed below, with a worked binary example you can reproduce in the tool.

Operator	Name	Example (binary)	Decimal
`+`	Addition	1010 + 0101 = 1111	10 + 5 = 15
`−`	Subtraction	1010 − 0011 = 0111	10 − 3 = 7
`×`	Multiplication	1010 × 0010 = 10100	10 × 2 = 20
`÷`	Division	1010 ÷ 0010 = 0101	10 ÷ 2 = 5
`%`	Modulo	1010 % 0011 = 0001	10 % 3 = 1
`&`	AND	1010 & 1100 = 1000	10 & 12 = 8
`\|`	OR	1010 \| 1100 = 1110	10 \| 12 = 14
`^`	XOR	1010 ^ 1100 = 0110	10 ^ 12 = 6
`«`	Left Shift	0001 « 4 = 10000	1 « 4 = 16
`»`	Right Shift	1000 » 2 = 0010	8 » 2 = 2

What the Tool Gives You

Results in Four Bases

Each answer is shown at once in binary, octal, decimal, and hexadecimal — no separate conversion step needed.

Large-Number Support

Calculations use BigInt, so very large binary values stay exact instead of losing precision.

Full Bitwise Set

AND, OR, XOR and both shift directions, alongside the five arithmetic operators.

Quick Examples

One-tap example expressions plus a built-in operator reference panel for fast recall.

Bitwise operators are binary-only. Arithmetic operators are available on every tab, but AND, OR, XOR, and shifts appear only on the Binary tab because they act directly on individual bits.

Frequently Asked Questions

What is binary?

Binary is a base-2 number system that uses only 0 and 1. Each digit represents a power of 2. For example, 1010 in binary equals 10 in decimal (8 + 2).

What are bitwise operations?

Bitwise operations work on individual bits. AND (&) returns 1 only if both bits are 1. OR (|) returns 1 if either bit is 1. XOR (^) returns 1 when the two bits differ.

How do shift operations work?

Left shift («) multiplies by 2 for each position moved; right shift (») divides by 2. For example, 0001 « 4 = 10000, which is 1 × 2⁴ = 16 in decimal.

Why are results shown in four bases?

The same value is displayed in binary, octal, decimal, and hexadecimal so you can read it in whichever base your task needs and copy any format with one click — useful when moving between code, math, and documentation.