How Binary Works: Binary Numbers Explained

Everything a computer does comes down to 1s and 0s. Binary looks alien at first, but it works exactly like the decimal system you already know — just with two digits instead of ten. Once that clicks, bits, bytes and hexadecimal all make sense.

Why computers use binary

Computers are built from billions of tiny switches that are either on or off. Two states map perfectly to two digits: 1 (on) and 0 (off). Representing data in base 2 is simply the most natural fit for the hardware, and it's robust — a circuit only has to tell "high" from "low," not ten different voltage levels.

Place values: base 2 vs base 10

In decimal (base 10), each position is a power of ten: ones, tens, hundreds. In binary (base 2), each position is a power of two: ones, twos, fours, eights, and so on. That's the only difference. Reading right to left, the binary number 1011 is:

• 1 × 8 = 8
• 0 × 4 = 0
• 1 × 2 = 2
• 1 × 1 = 1

Add them up: 8 + 0 + 2 + 1 = 11 in decimal.

Converting decimal to binary

To go the other way, repeatedly subtract the largest power of two that fits. For 13: the largest power of two ≤ 13 is 8, leaving 5; then 4, leaving 1; then 1. So you have 8 + 4 + 1, which is positions 8, 4, and 1 set: 1101. (There's also a divide-by-2 method, but the powers-of-two approach is more intuitive.)

Bits and bytes

A single binary digit is a bit. Eight bits make a byte, which can represent 2⁸ = 256 different values (0–255). That number is everywhere: a color channel, a character in older text encodings, one octet of an IPv4 address. Larger values just use more bytes.

Why hexadecimal rides along

Long binary strings are hard for humans to read, so programmers use hexadecimal as shorthand. Because 16 = 2⁴, one hex digit equals exactly four bits, and two hex digits equal one byte. So 11111111 becomes FF — much easier to handle. Binary, hex and decimal are just three views of the same value.

A note on negative numbers

Computers represent negative integers using a scheme called two's complement, where the highest bit indicates the sign and negation is done by flipping the bits and adding one. You don't need it for everyday conversions, but it's why an 8-bit signed number ranges from −128 to 127 rather than 0 to 255.

Try it

Convert between binary, octal, decimal and hex instantly with our number base converter, and turn text into its raw bytes with the hex ↔ text converter. For the hex side of the story, read hexadecimal explained.