--- title: "Restoring division of 31 by 13" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:restoring-31-13" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/restoring-31-13 site: BCT Engineering --- # Restoring division of 31 by 13 Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2079 Baisakh, 8 marks - Video: [Restoring Division Algorithm for Unsigned Integer](https://www.youtube.com/watch?v=PzV6gYpVLuc) — TutorialsPoint - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/restoring-31-13 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Explain the restoring division algorithm. Use this algorithm to divide 31 (dividend) by 13 (divisor). ## Short answer In restoring division, shift A,Q left, subtract divisor, restore by adding back if A is negative, and set Q0 accordingly. Dividing 31 by 13 gives quotient 2 (00010) and remainder 5 (000101). ## Answer #### Restoring division algorithm 1. Load A = 0, Q = dividend, M = divisor, SC = n. 2. Shift A and Q left by one bit (the MSB of Q goes into the LSB of A). 3. A = A − M. 4. If A < 0 (sign bit 1): set Q0 = 0 and **restore** A by adding M back (A = A + M). If A ≥ 0: set Q0 = 1. 5. SC = SC − 1. If SC ≠ 0 repeat from step 2. 6. At the end Q holds the quotient and A holds the remainder. #### 31 ÷ 13 Dividend = 31 = 11111 (Q), divisor M = 13 = 001101 (n+1 = 6 bits), A = 0, n = 5. ```text Step Action A Q - Initial 000000 11111 1 Shift left A,Q 000001 11110 A = A - M (1 - 13 = -12) 110100 11110 A<0: Q0=0, restore A 000001 11110 2 Shift left A,Q 000011 11100 A = A - M (3 - 13 = -10) 110110 11100 A<0: Q0=0, restore A 000011 11100 3 Shift left A,Q 000111 11000 A = A - M (7 - 13 = -6) 111010 11000 A<0: Q0=0, restore A 000111 11000 4 Shift left A,Q 001111 10000 A = A - M (15 - 13 = 2) 000010 10000 A>=0: Q0=1 000010 10001 5 Shift left A,Q 000101 00010 A = A - M (5 - 13 = -8) 111000 00010 A<0: Q0=0, restore A 000101 00010 ``` **Answer: 31 ÷ 13: quotient = 2 (00010), remainder = 5 (000101)** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why is M written with 6 bits (001101) for 31 / 13? A. Because 13 needs 6 bits B. Register A and the adder are n+1 = 6 bits C. To store the quotient D. To allow a negative divisor Answer: B. The dividend 31 has n = 5 bits so A and M are n+1 = 6 bits. (Key point: Divisor width) 2. In step 1 A = 1 - 13 = -12 is negative. What happens? A. Q0 = 1 and A stays -12 B. Q0 = 0 and A stays -12 C. Q0 = 0 and A is restored by adding M D. Q0 = 1 and M is subtracted again Answer: C. A < 0 means the divisor did not fit; restore A and set Q0 = 0. (Key point: Restore) 3. What is the quotient of 31 / 13? A. 2 (00010) B. 3 (00011) C. 1 (00001) D. 5 (00101) Answer: A. Only step 4 had A >= 0 (15 - 13 = 2), setting Q0 = 1, giving 00010 = 2. (Key point: Quotient) 4. What is the remainder, and the check? A. 2, since 13 x 5 + 2 = 67 B. 5, since 13 x 2 + 5 = 31 C. 5, since 13 x 2 + 5 = 26 D. 0, since 13 x 2 = 26 Answer: B. A ends as 000101 = 5; 26 + 5 = 31. (Key point: Remainder) ## Related in Computer Organization and Architecture - [Restoring division algorithm and hardware](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Arestoring-division) — Computer Organization and Architecture, chapter 5, asked 2× - [Signed division and non-restoring division](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Anonrestoring-division) — Computer Organization and Architecture, chapter 5 - [Non-restoring division of 10 by 5](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Anonrestoring-10-5) — Computer Organization and Architecture, chapter 5 - [Non-restoring division with flowchart](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Anonrestoring-explain) — Computer Organization and Architecture, chapter 5, asked 3× - [Restoring division of 10 by 3](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Arestoring-10-3) — Computer Organization and Architecture, chapter 5 - [Restoring vs non-restoring division](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Arestoring-vs-nonrestoring) — Computer Organization and Architecture, chapter 5, asked 5×