Question

cyrus decides to design a clock that shows all the numbers in binary, and is figuring out how many bits will be required to show the minutes. whats the least number of bits that youll need to represent 59 in binary?

Explanation:

Step1: Recall bit - number formula

To find the least number of bits \(n\) to represent a decimal number \(N\) in binary, we use the formula \(2^{n - 1}\leq N<2^{n}\). We need to find the smallest integer \(n\) such that \(2^{n-1}\leq39 < 2^{n}\).

Step2: Test values of \(n\)

• For \(n = 5\): \(2^{5-1}=2^{4} = 16\), \(2^{5}=32\). Since \(39\geq32\), \(n = 5\) is too small.
• For \(n=6\): \(2^{6 - 1}=2^{5}=32\), \(2^{6}=64\). We have \(32\leq39<64\), so this satisfies the inequality.

Answer:

6