Question

Suppose you want to encode the numerals 0–9 and the 26 letters of the alphabet, using separate codes for lowercase and uppercase letters. What is the minimum number of binary digits you will need for the code?
A.
5
B.
6
C.
7
D.
8
E.
9

Answer 1

Lets first work out how many different codes would be needed to represent everything. 26 for lowercase, 26 for uppercase, and 10 for 0-9. Total, that makes 62 needed codes.

If we start with 0, we need to go up to 61 to represent all the characters. Thus, we can convert 61 to binary and count the number of digits needed to represent that as the last number in the set and that will tell us how many digits are needed.

61 in binary is 111101, so we need 6 digits to represent that number. The answer is B.