Number Bases Explained: Binary, Decimal and Hexadecimal

By the Toolbench team · Updated September 2026

Decimal feels so natural that it is easy to forget it is just one choice among many possible number systems. Understanding what a "base" actually means makes binary and hexadecimal far less mysterious.

What "base" actually means

A number base defines how many unique digits are available before a new column is needed. Decimal (base 10) uses ten digits, 0 through 9, before rolling over into a new column. Binary (base 2) uses only two digits, 0 and 1. Hexadecimal (base 16) uses sixteen digits, 0 through 9 followed by A through F.

Why computers use binary

At the hardware level, a transistor is most reliably read as one of two states, roughly "on" or "off." Binary maps directly onto that physical reality, which is why it became the foundation of digital computing rather than an arbitrary design choice.

Why hexadecimal shows up alongside binary

Binary numbers get long and hard to read quickly, since representing even a modest value can take many digits. Hexadecimal was adopted as a more compact stand-in, because each single hex digit represents exactly four binary digits, making conversion between the two clean and predictable, unlike decimal.

A simple way to think about place value

In any base, each column represents a power of that base, just as decimal columns represent powers of ten (ones, tens, hundreds). In binary, columns represent powers of two (ones, twos, fours, eights), and in hexadecimal, powers of sixteen. The underlying logic is identical across all of them, only the number of digits per column changes.

Convert between bases

The Number Base Converter converts any number instantly between binary, octal, decimal, and hexadecimal, which is a fast way to build intuition by comparing the same value across bases side by side.