CSCI 370 Computer Architecture: Homework 2 Solutions

Due date: On or before Monday, March 25, 2024 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 73₈ (or 111011₂) and 35₈ (or 011101₂) 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 111011	011101	000000 000000
   1	Multiplier[0]=1 ⇒ ADD			000000 000000 + 000000 111011    000000 111011
   	SHL Multiplicand and SHR Multiplier	000001 110110	001110
   2	Multiplier[0]=0 ⇒ Do nothing.			000000 111011
   	SHL Multiplicand and SHR Multiplier	000011 101100	000111
   3	Multiplier[0]=1 ⇒ ADD			000000 111011 + 000011 101100    000100 100111
   	SHL Multiplicand and SHR Multiplier	000111 011000	000011
   4	Multiplier[0]=1 ⇒ ADD			000100 100111 + 000111 011000    001011 111111
   	SHL Multiplicand and SHR Multiplier	001110 110000	000001
   5	Multiplier[0]=1 ⇒ ADD			001011 111111 + 001110 110000    011010 101111
   	SHL Multiplicand and SHR Multiplier	011101 100000	000000
   6	Multiplier[0]=0 ⇒ Do nothing.			011010 101111
   	SHL Multiplicand and SHR Multiplier	111011 000000	000000




2. (Refined division: 50%) Using a table similar to that shown in the Slide 8.11, calculate the octal unsigned 6-bit integer 75₈ (or 111101₂) divided by another octal unsigned 6-bit integer 13₈ (or 001011₂) 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	111101	001011
   1	Shift left; Difference	000001	111010	001011	000001  – 001011         110110 < 0
   	Difference < 0 ⇒ Do nothing.
   2	Shift left; Difference	000011	110100	001011	000011  – 001011         111000 < 0
   	Difference < 0 ⇒ Do nothing.
   3	Shift left; Difference	000111	101000	001011	000111  – 001011         111100 < 0
   	Difference < 0 ⇒ Do nothing.
   4	Shift left; Difference	001111	010000	001011	001111  – 001011         000100 ≥ 0
   	Rem = Diff; Set lsb of quotient.	000100	010001
   5	Shift left; Difference	001000	100010	001011	001000  – 001011         111101 < 0
   	Difference < 0 ⇒ Do nothing.
   6	Shift left; Difference	010001	000100	001011	010001  – 001011         000110 ≥ 0
   	Rem = Diff; Set lsb of quotient.	000110	000101