--- title: "Booth multiplication of 9 × -3" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:booth-9x-3" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/booth-9x-3 site: BCT Engineering --- # Booth multiplication of 9 × -3 Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2071 Shrawan, 5 marks - 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/booth-9x-3 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Illustrate the multiplication of 9 and -3 using 2's complement method (Booth's algorithm). ## Short answer M=9=01001, Q=-3=11101, -M=10111, 5 bits. Execute: 10 A−M, 01 A+M, 10 A−M, two steps no change, each with ASR. Result A,Q = 11111 00101 = -27. ## Answer Signed numbers are held in 2's complement form and Booth's algorithm handles the sign automatically (10 → A − M, 01 → A + M, then ASR). 5 bits are needed. Multiplicand M = 9 = 01001, multiplier Q = -3 = 11101, -M = 10111, n = 5 bits. ```text Step Action A Q Q-1 - Initial 00000 11101 0 1 Q0Q-1=10: A = A - M 10111 11101 0 ASR 11011 11110 1 2 Q0Q-1=01: A = A + M 00100 11110 1 ASR 00010 01111 0 3 Q0Q-1=10: A = A - M 11001 01111 0 ASR 11100 10111 1 4 Q0Q-1=11: no change 11100 10111 1 ASR 11110 01011 1 5 Q0Q-1=11: no change 11110 01011 1 ASR 11111 00101 1 ``` Result in A,Q = 11111 00101 = -27. **Answer: 9 × -3 = -27** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For M = 9 = 01001, what is -M? A. 10110 B. 10111 C. 11001 D. 01111 Answer: B. 2's complement of 01001 is 10111. (Key point: -M value) 2. Multiplier -3 = 11101 starts with Q0 Q-1 = 10. What happens? A. A = A + M giving 01001 B. No change C. A = A - M giving 10111 D. A = 0 and shift Answer: C. Pair 10 means subtract M, so A = 00000 + 10111. (Key point: First step) 3. What is the final product of 9 x -3? A. -27 = 11111 00101 B. 27 = 00000 11011 C. -27 = 00000 11011 D. -18 = 11111 01110 Answer: A. A:Q = 11111 00101 = -27. (Key point: Result) ## Related in Computer Organization and Architecture - [Booth multiplication algorithm and hardware](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-algorithm) — Computer Organization and Architecture, chapter 5, asked 8× - [Booth multiplication of -5 × -9](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-5x-9) — Computer Organization and Architecture, chapter 5, asked 5× - [Booth multiplication of 5 × -6](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-5x-6) — Computer Organization and Architecture, chapter 5, asked 5× - [Booth multiplication of -7 × -10](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-7x-10) — Computer Organization and Architecture, chapter 5, asked 5× - [Booth multiplication of 10 × (-5)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-10x-5) — Computer Organization and Architecture, chapter 5, asked 5× - [Booth multiplication of -6 × -11](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-6x-11) — Computer Organization and Architecture, chapter 5, asked 5×