Why is number of bits always a power of two?

Question

We have 8-bit, 16-bit, 32-bit and 64-bit hardware architectures and operating systems. But not, say, 42-bit or 69-bit ones.Why? Is it something fundamental that makes 2^n bits a better choice, or is just about compatibility with existing systems?

Answer 1

Neither, it is the numbering system.

Base 10 is decimal. the digits are 0..9 , which are the remainders when dividing any number by 10.

So 123 = 100 + 20 + 3 = 10^2 + 2*10^1 + 3*10^0

Binary goes by powers of 2. The digits are 0 and 1 which are the remainders when dividing any number by 2.

So the powers of 2 are 1,2,4,8,16,32,64,128,256, etc

so decimal 123 is converted as 123 = 64 + 32 + 16 + 8 + 2 + 1 = 01111011

4 bits = 1/2 byte = 1 nibbl

8 bits is 1 byte

16 bits is 2 bytes

24 bits is 3 bytes

32 bits is 4 bytes

Because of that, 1 byte = 8 bits, it shall always be multiples of 8 and base 2