--- title: "Booth multiplication of -5 × -9" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:booth-5x-9" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/booth-5x-9 site: BCT Engineering --- # Booth multiplication of -5 × -9 Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2072 Chaitra, 5 marks - Video: [COA | ALU | Multiplication | Booth's Algorithm | Bharat Acharya Education](https://www.youtube.com/watch?v=vcvgvqnH7GA) — Bharat Acharya Education - 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-5x-9 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Multiply -5 × -9 using Booth's multiplication algorithm. ## Short answer M=-5=11011, Q=-9=10111, -M=00101, 5 bits. Steps: 10→A−M, 11→no change, 11→no change, 01→A+M, 10→A−M, with ASR after each. Result A,Q = 00001 01101 = 45. ## Answer Booth's rule: 10 → A = A − M, 01 → A = A + M, 00/11 → no change; then ASR of A, Q, Q-1. Five bits are needed for the signed numbers. Multiplicand M = -5 = 11011, multiplier Q = -9 = 10111, -M = 00101, n = 5 bits. ```text Step Action A Q Q-1 - Initial 00000 10111 0 1 Q0Q-1=10: A = A - M 00101 10111 0 ASR 00010 11011 1 2 Q0Q-1=11: no change 00010 11011 1 ASR 00001 01101 1 3 Q0Q-1=11: no change 00001 01101 1 ASR 00000 10110 1 4 Q0Q-1=01: A = A + M 11011 10110 1 ASR 11101 11011 0 5 Q0Q-1=10: A = A - M 00010 11011 0 ASR 00001 01101 1 ``` Result in A,Q = 00001 01101 = 45. **Answer: -5 × -9 = 45** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For M = -5 = 11011, what is -M? A. 11010 B. 00100 C. 00101 D. 10101 Answer: C. 2's complement of 11011 is 00101 (= +5). (Key point: -M value) 2. The multiplier -9 = 10111 has Q0 Q-1 = 10 at the start. What is done? A. A = A - M, i.e. A = 00101 B. A = A + M, i.e. A = 11011 C. No arithmetic D. A = A - M, i.e. A = 11011 Answer: A. Pair 10 means subtract M: A = 0 + 00101 = 00101. (Key point: First step) 3. Why is -5 x -9 positive (45)? A. Booth always gives a positive result B. Both operands are negative, and 2's complement Booth handles signs automatically C. The sign bit is discarded D. Only the multiplicand sign counts Answer: B. Negative x negative is positive; the final A:Q = 00001 01101 = 45. (Key point: Sign of product) ## Close variants set in other exams - [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× ## 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 with hardware](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-hardware) — Computer Organization and Architecture, chapter 5 - [Booth multiplication of -6 × 12](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-6x12) — Computer Organization and Architecture, chapter 5 - [Booth multiplication of 23 × -21 (6 bits)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-23x-21) — Computer Organization and Architecture, chapter 5 - [Booth multiplication of 6 × 7](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-6x7) — Computer Organization and Architecture, chapter 5 - [Booth multiplication 7×3](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_organization_and_architecture%3Abooth-7x3) — Computer Organization and Architecture, chapter 5, asked 2×