Question

What is the minimum number of bits needed to store the decimal value 200?

10
9
8
6
5

Answer 1

8 bits

Step-by-step explanation:

Given

Decimal Value = 200

Required

Determine minimum number of bits to store the value

Represent the decimal value with N and the number of bits with n

The relationship between n and N is:

`2^n = N`

Substitute 200 for N

`2^n = 200`

Take Log of both sides

`Log2^n = Log200`

Apply law of indices

`nLog2 = Log200`

Make n the subject

`n = (Log200)/(Log2)`

`n = 7.64385618977`

We need n to be an integer; So, we have to approximate

`n = 8`