How Binary Works

Binary is the base-2 number system — it uses only two digits: 0 and 1. Every digital computer, from your phone to a supercomputer, stores and processes all data as binary numbers.

Why Binary?

Electronic circuits have two reliable states: on and off, which map to 1 and 0. Using more states (like base-10) would require precise voltage levels that are hard to maintain reliably. Binary is robust: anything above a threshold is 1, anything below is 0.

Place Values

Just as decimal uses powers of 10 (1, 10, 100, 1000...), binary uses powers of 2 (1, 2, 4, 8, 16, 32, 64, 128...). The rightmost digit is the 2⁰ place (value 1). Moving left: 2¹ (2), 2² (4), 2³ (8), and so on.

Reading Binary Numbers

To read a binary number, multiply each digit by its place value and sum the results. Binary 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13 in decimal.

Bits, Bytes, and Beyond

A single binary digit is a bit. Eight bits make a byte, which can hold values 0–255. A byte is the fundamental unit of computer memory. 1 kilobyte = 1024 bytes = 2¹⁰ bytes.

Common Binary Values

Memorizing a few values helps: 8 = 1000, 16 = 10000, 32 = 100000, 64 = 1000000, 128 = 10000000, 255 = 11111111, 256 = 100000000. Notice that powers of 2 always have exactly one 1-bit.