Question

1. Given n bits, how many unsigned integers can be represented with the n bits?
   What is the range of these integers? (6 points)

2. There are 26 characters in the alphabet we use for writing English. What is the least number of bits needed to give each character a unique bit pattern?
   How many bits would we need to distinguish between upper- and lowercase versions of all 26 characters? (12 points)

Answer 1

1. a) Given n bits, how many unsigned integers can be represented with the n bits?

Answer: 2^n

Explanation
_ _ _ _ _ _ ... n
1 2 3 4 ....... n

n bits -> n places
Each place can hold either 0/1 which means 2 possibilities.
So, for n places 2^n possible unsigned integers are there

1.b) What is the range of these integers? (6 points)

Unsigned integers mean they don't have a sign. So, they start from 0

Least number = 000 ... 000 (for n bits) = 0
Highest number = 111 ... 111 (for n bits) = 2^(n+1) - 1

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