Which number system does a typical 32-bit digital computer use internally?

Concept

A positional number system has radix b; the place with index k has weight bk.

Digital hardware stores each bit in one of two stable states, conventionally represented as 0 and 1.

Application

1. The term 32-bit describes the width of a word or data path: it contains 32 individual bits.

2. Each of those bits has two possible values, so the underlying radix is 2.

Contrast

• Base 8 is octal notation; one octal digit compactly represents three binary bits.

• Base 10 is decimal notation commonly used for human arithmetic.

• Base 16 is hexadecimal notation; one hexadecimal digit compactly represents four binary bits.

Cross-check

A 32-bit word can form 232 distinct bit patterns, because every one of its 32 positions has two choices.

Result

Therefore, the number system used internally is base 2 (binary).