Binary Calculator — Arithmetic & Decimal Conversion

Binary Calculator

Binary arithmetic, with decimal equivalents shown alongside.

First binary number

= 13 in decimal

Operation

Second binary number

= 6 in decimal

Result (binary)

10011

= 19 in decimal

Only 0s and 1s are valid binary digits — each position represents a power of 2, the same way each decimal position represents a power of 10.

A worked example

1101 (13) plus 110 (6) equals 10011 in binary — 19 in decimal.

Frequently asked questions

Why does binary only use 0 and 1?

Binary is base-2, meaning each position represents a power of 2 rather than a power of 10 like decimal — with only two possible digits, it maps directly onto the on/off states a computer's circuits naturally use.

How do I read a binary number?

Each digit's position represents a power of 2, counting from the right: 1, 2, 4, 8, 16, and so on. Add up the powers of 2 where there's a 1 — 1101 means 8+4+0+1 = 13.