CSCI 370 Computer Architecture: Homework 2 Solutions

Due date: On or before Wednesday, April 01, 2026 Absolutely no copying others’ works

Name: _____Professor Hu_____

• Upload the completed homework to the section of “COVID-19 Exams, Homeworks, & Programming Exercises” of Blackboard.
• There are four algorithms discussed totally for multiplication and division.  Make sure you are using the correct ones for the following two questions. 
• The purpose of homeworks is for students to practice for the exams without others’ help, so the penalty of mistakes will be minor.
• Without practicing for the exams properly, students will not be able to do well on the exams.

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1. (Sequential/first-version multiplication: 50%) Using a table similar to that shown in the Slide 8.5, calculate the product of the octal unsigned 6-bit integers 53₈ (or 101011₂) and 75₈ (or 111101₂) using the hardware and algorithm described in the figures of Slide 8.5. You should show the contents of each register on each step.
   Ans>
   
   
   This question is to simulate the computer hardware, so
   
   
   • each number is either 12 or 6 bits, and
   • has to complete the 6 steps.
   
   

   Iteration		Multiplicand	Multiplier	Product
   0	Initialize	000000 101011	111101	000000 000000
   1	Multiplier[0]=1 ⇒ ADD			000000 000000 + 000000 101011    000000 101011
   	SHL Multiplicand and SHR Multiplier	000001 010110	011110
   2	Multiplier[0]=0 ⇒ Do nothing.			000000 101011
   	SHL Multiplicand and SHR Multiplier	000010 101100	001111
   3	Multiplier[0]=1 ⇒ ADD			000000 101011 + 000010 101100    000011 010111
   	SHL Multiplicand and SHR Multiplier	000101 011000	000111
   4	Multiplier[0]=1 ⇒ ADD			000011 010111 + 000101 011000    001000 101111
   	SHL Multiplicand and SHR Multiplier	001010 110000	000011
   5	Multiplier[0]=1 ⇒ ADD			001000 101111 + 001010 110000    010011 011111
   	SHL Multiplicand and SHR Multiplier	010101 100000	000001
   6	Multiplier[0]=1 ⇒ ADD			010011 011111 + 010101 100000    101000 111111
   	SHL Multiplicand and SHR Multiplier	101011 000000	000000

   
   ^†You may double-check the answer as follows:
   
   538×758 = 1010112×1111012 = 43×61 = 2623 = 101000 1111112


2. (Refined division: 50%) Using a table similar to that shown in the Slide 8.11, calculate the octal unsigned 6-bit integer 73₈ (or 111011₂) divided by another octal unsigned 6-bit integer 11₈ (or 001001₂) using the hardware and algorithm described in the figures of Slide 8.11. You should show the contents of each register on each step.
   ^†Note that you have to actually show the differences in the procedures, not just the signs.
   Ans>
   
   

   Iteration		Remainder	Quotient	Divisor	Difference
   0	Initialize	000000	111011	001001
   1	Shift left; Difference	000001	110110	001001	000001  – 001001  ⇓    000001  + 110111         111000 < 0
   	Difference < 0 ⇒ Do nothing.
   2	Shift left; Difference	000011	101100	001001	000011  – 001001  ⇓    000011  + 110111         111010 < 0
   	Difference < 0 ⇒ Do nothing.
   3	Shift left; Difference	000111	011000	001001	000111  – 001001  ⇓    000111  + 110111         111110 < 0
   	Difference < 0 ⇒ Do nothing.
   4	Shift left; Difference	001110	110000	001001	001110  – 001001  ⇓    001110  + 110111       1 000101 ≥ 0
   	Rem = Diff; Set lsb of quotient.	000101	110001
   5	Shift left; Difference	001011	100010	001001	001011  – 001001  ⇓    001011  + 110111      1 000010 ≥ 0
   	Rem = Diff; Set lsb of quotient.	000010	100011
   6	Shift left; Difference	000101	000110	001001	000101  – 001001  ⇓    000101  + 110111         111100 < 0
   	Difference < 0 ⇒ Do nothing.

   
   ^†You may double-check the answer as follows:
   
   738÷118 = 1110112÷0010012 = 59÷9 ⇒ Q: 6 = 0001102 and R: 5 = 0001012