1a what is the minimum number of bits that are required to

Question

1a. What is the minimum number of bits that are required to uniquely represent the characters of English alphabet? (Consider upper case characters alone)

The number of unique bit patterns using i bits is 2ⁱ We need at least 26 unique bit patterns. The cleanest approach is to compute log₂ 26 and take the ceiling .This yields 5 as the answer. Trial and error is also an acceptable solution.

1b. how many more characters can be uniquely represented without requiring additional bits?

With 5 bits, we can represent up to 32 (2⁵) unique bit patterns; we can represent

32 - 26 = 6 more characters without requiring additional bits.

2 Using 7 bits to represent each number, write the representations of 23 and -23 in signed

Magnitude and 2's complement integers.

	Signed Magnitude	1's Complement	2's Complement
23	0010111	0010111	0010111
-23	1010111	1101000	1101001