Homework 1 Solutions

Problem 1

1. Minimum number of bits required = 6, since 2⁵ = 32 < 49 < 64 = 2⁶
2. 64 – 49 = 15 more students can be added

1. Largest positive number in 16-bit two’s complement is 0111 1111 1111 1111 which corresponds to 2¹⁵ - 1 = 32767.
2. The greatest magnitude negative number that can be represented in 16-bit two’s complement is 1000 0000 0000 0000 which corresponds to – (2¹⁵ ) = – 32768.
3. Largest positive number in n-bit two’s complement code is 2^n-1 - 1
4. Greatest magnitude negative number in n-bit two’s complement code – (2^n-1 )

1. 01011010 + 01110110 = 11010000 = 0xD0 ; no overflow
2. 11010011 + 00110111 = 00001010 = 0x0A ; overflow
3. 01110111 + 01111100 = 11110011 = 0xF3 ; no overflow
4. 01100110 + 10101010 = 00010000 = 0x10 ; overflow

1. NOT(NOT(1001)) AND NOT(1101)

Þ NOT(0110) AND 0010

Þ 1001 AND 0010

Þ 0000 = x0

2. (NOT(1100) AND NOT(1001)) OR 0101

Þ (0011 AND 0110) OR 0101

Þ 0010 OR 0101

Þ 0111 = x7

3. NOT (1101 AND NOT(0001))

Þ NOT (1101 AND 1110)

Þ NOT (1100)

Þ 0011 = x3

4. NOT(((0101 OR 1100) OR 0001) AND 1001)

Problem 6

Problem 7

Problem 8

Problem 9