how many possible values can we have with the 8 bits in a byte?

An 8-bit byte can represent 256 different possible values.

Quick Scoop: The Core Idea

Each of the 8 bits can be either 0 or 1, so the total number of combinations is given by:

28=2562^{8}=25628=256

That means an 8-bit byte can encode 256 unique patterns of bits, from 00000000 to 11111111.

Mini breakdown

• 1 bit → 2 values (0, 1) ⇒21\Rightarrow 2^{1}⇒21
• 2 bits → 4 values ⇒22\Rightarrow 2^{2}⇒22
• 3 bits → 8 values ⇒23\Rightarrow 2^{3}⇒23
• …
• 8 bits → 256 values ⇒28\Rightarrow 2^{8}⇒28

In binary, those 256 values typically cover decimal numbers from 0 to 255 when used as an unsigned byte.

Common confusion (why not 255?)

People sometimes add powers of two:

20+21+⋯+27=2552^{0}+2^{1}+\dots +2^{7}=25520+21+⋯+27=255

That sum gives the maximum number you can represent (255), not how many distinct values there are. The number of distinct combinations is still 28=2562^{8}=25628=256, because you also count 0 as one of the values.

Think of it like numbered lockers: if the lockers are labeled 0 through 255, you still have 256 lockers total.

Tiny extra: signed vs unsigned

• Unsigned 8-bit: 0 to 255 → 256 values.

• Signed 8-bit (two’s complement): −128-128−128 to +127+127+127 → still 256 values, just split into negative and positive.

TL;DR: With 8 bits in a byte, you can have 256 possible values.

Information gathered from public forums or data available on the internet and portrayed here.