Binary Calculator

Perform arithmetic and bitwise operations on binary numbers. This calculator adds, subtracts, multiplies, divides, and handles logic operations for binary values. Essential for computer science and digital logic work.

Operation Type

First Binary Number

Second Binary Number

Operation

Result

Enter binary numbers to see the result

About Binary Operations

Arithmetic operations work like regular math but in base-2.Bitwise operations compare individual bits: AND (both must be 1), OR (at least one is 1), XOR (exactly one is 1), and NOT (inverts all bits).

How It Works

This binary calculator performs arithmetic and bitwise operations directly on binary numbers. It handles addition, subtraction, multiplication, division, and logical operations (AND, OR, XOR, NOT) with step-by-step results.

The calculation process:

Input binary values: Enter two binary numbers for the operation.
Select operation: Choose arithmetic (+, -, ×, ÷) or bitwise (AND, OR, XOR, NOT).
Perform calculation: The operation is performed using binary arithmetic rules.
Display results: Show result in binary, with optional decimal and hex equivalents.

Binary addition follows: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1). Binary multiplication is simpler than decimal - each digit is either 0 or 1, so partial products are either 0 or the multiplicand.

When You'd Actually Use This

Learning Binary Arithmetic

Understand how addition, subtraction, and other operations work in base-2.

Digital Logic Design

Verify binary calculations for circuit design and ALU (Arithmetic Logic Unit) development.

Assembly Programming

Calculate binary values for low-level programming and understand CPU arithmetic.

Computer Architecture Studies

Explore how computers perform arithmetic at the hardware level.

Bitwise Operation Practice

Master AND, OR, XOR, NOT operations used in programming and digital systems.

CTF Challenge Solving

Perform binary calculations for cryptography and reverse engineering challenges.

What to Know Before Using

Binary addition uses carries

When you add 1+1, the result is 10 (0 with carry 1). Multiple carries can propagate left.

Subtraction uses borrowing

When subtracting 0-1, borrow from the next position. Or use 2's complement: A-B = A + (-B).

Bitwise vs arithmetic operations differ

AND/OR/XOR work bit-by-bit independently. Arithmetic operations involve carries and borrows across bits.

Overflow can occur

Fixed-width binary has maximum values. 8-bit max is 255. Adding 255+1 = 0 (overflow/wrap-around).

Division may have remainders

Binary division works like long division. Result may have a remainder, just like decimal division.

Common Questions

How does binary addition work?

Same as decimal but simpler: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1).

What's 1+1 in binary?

10 (which is 2 in decimal). In binary, there's no digit '2', so we carry: 1+1 = 10.

How do bitwise operations work?

AND: both 1 = 1. OR: either 1 = 1. XOR: exactly one 1 = 1. NOT: flip all bits. Each bit is independent.

What's binary multiplication?

Simpler than decimal! Each digit is 0 or 1, so partial products are either 0 or the multiplicand. Then add them up.

How does binary division work?

Like long division. See how many times divisor fits into portions of dividend. Quotient digits are 0 or 1.

What's 2's complement subtraction?

A - B = A + (2's complement of B). Invert B's bits and add 1, then add to A. Discard overflow carry.

Why learn binary arithmetic?

It's how computers calculate. Understanding binary arithmetic helps with programming, debugging, and digital design.

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