Calculating bits required to store decimal number

Question

This is a homework question that I am stuck with.

Consider unsigned integer representation. How many bits will be required to store a decimal number

Answer 1

Assuming that the question is asking what's the minimum bits required for you to store

1. 3 digits number

My approach to this question would be:

• what's the maximum number of 3 digits number we need to store? Ans: 999
• what's the minimum amount of bits required for me to store this number?

This problem can be solved this way by dividing 999 by 2 recursively. However, it's simpler to use the power of maths to help us. Essentially, we're solving n for the equation below:

2^n = 999
nlog2 = log999
n ~ 10

You'll need 10 bits to store 3 digit number.

Use similar approach to solve the other subquestions!

Hope this helps!