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How Computers Represent and Process Information

Manual: General · Subject: Computer Science

Learn how binary, bits, bytes, and numeric representation shape the way computers store and manipulate data.

From physical signals to bits

Binary foundations

Digital computers encode information using two stable states, commonly represented as 00 and 11. A bit is one binary digit, and a byte is 88 bits. Larger units often scale by powers of two, so 1 KiB=1024 bytes1\,\text{KiB} = 1024\,\text{bytes} and 1 MiB=1024 KiB1\,\text{MiB} = 1024\,\text{KiB}.

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Why binary works

Binary is robust because electronic circuits can distinguish between two voltage ranges more reliably than many finely spaced levels.

Integers and negatives

Unsigned integers encode only nonnegative values, while signed integers usually use two's complement. For an nn-bit two's complement integer, the range is −2n−1-2^{n-1} to 2n−1−12^{n-1}-1. This representation simplifies arithmetic in hardware.

Common data representations

TypeExampleNotes
Binary integer1011012101101_2Base-2 number
ASCII character6565 for 'A'Older character encoding
Unicode character'你'Supports many languages
Floating-point3.143.14Approximate real-number encoding

How many bits are in a byte?

What is the range of an 88-bit signed two's complement integer?

Floating-point approximation

Many real numbers are stored in floating-point form, which trades exactness for a wide range of values. This is why 0.1+0.20.1 + 0.2 can produce a value that is very close to, but not exactly, 0.30.3 in many programming languages.

Why can floating-point arithmetic produce rounding error?

Why is two's complement popular in computer hardware?