Assignment #7 Key, Multiplication and Division Problems

John Visser CS 2560 Assignment #7 Key, Multiplication and Division Problems a) 6 * 2 = 0110 * 0010

Iter Step Product Multiplicand 0. initialize 0000 0010 0110

1. 0 -> no op 0000 0010 sr product 0000 0001 + 0110 2. 1 -> add cand 0110 0001 sr product 0011 0000

3. 0 -> no op 0011 0000 sr product 0001 1000

4. 0 -> no op 0001 1000 sr product 0000 1100 = 12 b) 2 * 7 = 0010 * 0111

Iter Step Product Multiplicand 0. initialize 0000 0111 0010 + 0010 1. 1 -> add cand 0010 0111 sr product 0001 0011 + 0010 2. 1 -> add cand 0001 0011 sr product 0001 1001 + 0010 3. 1 -> add cand 0001 1001 sr product 0001 1100

4. 0 -> no op 0001 1100 sr product 0000 1110 = 14 c) 5 * 3 = 0101 * 0011

Iter Step Product Multiplicand 0. initialize 0000 0011 0101 + 0101 1. 1 -> add cand 0101 0011 sr product 0010 1001 + 0101 2. 1 -> add cand 0111 1001 sr product 0011 1100

3. 0 -> no op 0011 1100 sr product 0001 1110

4. 0 -> no op 0001 1110 sr product 0000 1111 = 15 d) 7 / 2 = 0111 / 0010

Iter Step Remainder Divisor 0. initialize 0000 0111 0010 sl remainder 0000 1110 - 0010 1. subtract div 1110 1110 rem < 0, restore & sl 0001 1100 - 0010 2. subtract div 1111 1100 rem < 0, restore & sl 0011 1000 - 0010 3. subtract div 0001 1000 rem > 0, sl rem, add 1 0011 0001 - 0010 4. subtract div 0001 0001 rem > 0, sl rem, add 1 0010 0011 5. sr left half of remainder 0001 0011 = 3, remainder 1 e) 13 / 3 = 1101 / 0011

Iter Step Remainder Divisor 0. initialize 0000 1101 0011 sl remainder 0001 1010 - 0011 1. subtract div 1110 1010 rem < 0, restore & sl 0011 0100 - 0011 2. subtract div 0000 0100 rem > 0, sl rem, add 1 0000 1001 - 0011 3. subtract div 1101 1001 rem < 0, restore & sl 0001 0010 - 0011 4. subtract div 1110 0010 rem < 0, restore & sl 0010 0100 5. sr left half of remainder 0001 0100 = 4, remainder 1 f) 11 / 4 = 1011 / 0100

Iter Step Remainder Divisor 0. initialize 0000 1011 0100 sl remainder 0001 0110 - 0100 1. subtract div 1101 0110 rem < 0, restore & sl 0010 1100 - 0100 2. subtract div 1110 1100 rem < 0, restore & sl 0101 1000 - 0100 3. subtract div 0001 1000 rem > 0, sl rem, add 1 0011 0001 - 0100 4. subtract div 1111 0001 rem < 0, restore & sl 0110 0010 5. sr left half of remainder 0011 0010 = 2, remainder 3