Bitwise Binary Calculator - AND, OR, XOR & Bit Shift

Arithmetic & Bitwise Math in Base 2

This binary calculator runs arithmetic and bitwise operations directly on base-2 numbers, so you never have to convert to decimal by hand. Binary is built from just two digits — 0 and 1 — where each position stands for a power of 2.

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 bits directly, then read the answer in whichever base you need.

Who It's For

Programmers

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

Students

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

Networking

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

How to Calculate in Binary

Enter the First Number

Type the first value using only the digits 0 and 1. The 0b prefix is added automatically, so you only enter the bits. Invalid characters are flagged as you type.

Choose an Operator

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

Enter the Second Number

Type the second binary value into the lower field. For a shift operation, this is the number of positions to move, entered as a plain decimal count.

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: Tap a ready-made example to load an expression, then tweak the values to watch the result change across all four bases.

Operators & Features

Every operator the calculator supports is listed below, each 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. The five arithmetic operators work on every tab, but AND, OR, XOR and shifts appear only on the Binary tab because they act directly on individual bits.

Private by design: every calculation runs in your browser. Nothing you type is uploaded or sent to a server.

Frequently Asked Questions

How do you add two binary numbers?

Add column by column from the right, carrying when a column reaches 2: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1). For example, 1010 + 0101 = 1111, which is 10 + 5 = 15. Enter both numbers here and the tool does the carrying for you.

Can I subtract, multiply and divide in binary too?

Yes. All five arithmetic operators work directly on binary values: addition (+), subtraction (−), multiplication (×), division (÷) and modulo (%). Division and modulo by zero are caught and reported instead of crashing.

What do the bitwise AND, OR and XOR operators do?

They compare two numbers bit by bit. AND (&) returns 1 only when both bits are 1; OR (|) returns 1 when either bit is 1; XOR (^) returns 1 only when the two bits differ. These are the basis of masks and flag toggles.

What is a bitwise left or right shift?

A shift moves every bit sideways. Left shift («) multiplies by 2 for each place moved; right shift (») divides by 2. For example, 0001 « 4 = 10000, i.e. 1 × 2⁴ = 16. The second field is the number of positions to shift, entered as a decimal count.

Why is the result shown in four bases at once?

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

Can it handle very large binary numbers?

Yes. The calculator computes with BigInt, so large binary values stay exact rather than being rounded the way standard floating-point numbers would be.