Binary Calculator

Perform binary addition, subtraction, multiplication, and division. Convert between binary, decimal, octal, and hex with step-by-step explanations and bit visualization.

Sign Mode

Operation

Add

Operands

Value A

= 10 (unsigned 8-bit)

Value B

= 6 (unsigned 8-bit)

Result in All Bases

Binary

0001 0000

Decimal

Octal

0o20

Hexadecimal

0x10

Bit Visualization

Bit	7	6	5	4	3	2	1	0
A	0	0	0	0	1	0	1	0
B	0	0	0	0	0	1	1	0

+	0	0	0	1	0	0	0	0

Step-by-Step Solution

  0000 1010  (10)
+ 0000 0110  (6)
───────────
= 0001 0000  (16)

Quick Reference

AND (&)

Both bits must be 1 for result 1. Used to mask/clear bits.

OR (|)

Either bit being 1 gives 1. Used to set specific bits.

XOR (^)

Different bits give 1, same give 0. Used to toggle bits.

Two's Complement

Signed integers use MSB as sign. Negate by flipping bits + 1.

Left Shift (<<)

Shifts bits left, fills with 0s. Equivalent to multiplying by 2^n.

Right Shift (>>)

Shifts bits right. Logical fills with 0s; arithmetic preserves sign.

How to Use Binary Calculator

1Enter binary numbers or switch to decimal input.
2Select the arithmetic operation.
3View the result in all number bases.
4Review the step-by-step calculation.

Frequently Asked Questions

How do I add binary numbers?▾

Binary addition follows the same rules as decimal but with only 0 and 1: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry 1). Work from right to left, carrying as needed.

How do I convert binary to decimal?▾

Multiply each digit by 2 raised to its position (starting from 0 on the right). Example: 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.

What is two's complement?▾

Two's complement represents negative numbers in binary. Flip all bits and add 1. For example, -5 in 8-bit is: 5=00000101, flip=11111010, +1=11111011.

About Binary Calculator

Perform binary addition, subtraction, multiplication, and division. Convert between binary, decimal, octal, and hex with step-by-step explanations and bit visualization.

NexTool's Binary Calculator is completely free to use with no sign-up required. Your data is processed directly in your browser and never sent to our servers, ensuring complete privacy and instant results.