--- title: "Booth multiplication of 5 × -6" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:booth-5x-6" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/booth-5x-6 site: BCT Engineering --- # Booth multiplication of 5 × -6 Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2071 Chaitra, 4 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-5x-6 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Multiply 5 and -6 using the Booth multiplication algorithm. ## Short answer M=5=0101, Q=-6=1010, -M=1011, 4 bits. Sequence: 00 no change, 10 A−M, 01 A+M, 10 A−M, each with ASR. Final A,Q = 1110 0010 = -30. ## Answer Booth's algorithm with 4-bit registers. Multiplicand M = 5 = 0101, multiplier Q = -6 = 1010, -M = 1011, n = 4 bits. ```text Step Action A Q Q-1 - Initial 0000 1010 0 1 Q0Q-1=00: no change 0000 1010 0 ASR 0000 0101 0 2 Q0Q-1=10: A = A - M 1011 0101 0 ASR 1101 1010 1 3 Q0Q-1=01: A = A + M 0010 1010 1 ASR 0001 0101 0 4 Q0Q-1=10: A = A - M 1100 0101 0 ASR 1110 0010 1 ``` Result in A,Q = 1110 0010 = -30. **Answer: 5 × -6 = -30** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Why can 4-bit registers be used for 5 x -6? A. Booth needs only half the bits B. Both fit in 4-bit 2's complement (5 = 0101, -6 = 1010) C. The sign is stored separately D. Because the product is 4 bits Answer: B. Both operands lie in the 4-bit signed range -8..7, so n = 4 cycles. (Key point: Register size) 2. For M = 5 = 0101, what is -M? A. 1011 B. 1010 C. 0101 D. 1101 Answer: A. 2's complement of 0101 is 1011. (Key point: -M value) 3. What is 5 x -6 with its 8-bit A:Q form? A. 30 = 0001 1110 B. -30 = 0001 1110 C. -30 = 1110 0010 D. -24 = 1110 1000 Answer: C. After 4 cycles A:Q = 1110 0010 = -30. (Key point: Result) ## Close variants set in other exams - [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 -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×