4 You need to represent 2049 different street names How many

4 You need to represent 2,049 different street names. How many bits will this take if you give each street a different binary number?

Solution

As each street is given different binary number, and there are 2049 street names.

So, in total there will be 2049 different binary numbers.

Now with n-bits, we can represent 2ⁿ Binary Numbers.

With 11-bits, we can form:

2¹¹ bits = 2048 binary numbers

But here we required 2049 binary numbers, so require 1 more bit as with:

2¹² bits we can represent upto 4096 binary numbers.

Hence in the given question we require 12-bits to represent street names with 2049 different binary numbers.