--- title: "Booth multiplication of -6 × -11" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:booth-6x-11" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/booth-6x-11 site: BCT Engineering --- # Booth multiplication of -6 × -11 Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2075 Chaitra, 6 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-6x-11 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Multiply -6 × -11 using Booth's multiplication algorithm. ## Short answer Booth's algorithm with 5-bit registers: -6 (11010) × -11 (10101), -M=00110. After five add/subtract and arithmetic right shifts, result in A,Q is 00010 00010 = 66. ## Answer Booth's algorithm with 5-bit registers (−6 = 11010, −11 = 10101). Multiplicand M = -6 = 11010, multiplier Q = -11 = 10101, -M = 00110, n = 5 bits. ```text Step Action A Q Q-1 - Initial 00000 10101 0 1 Q0Q-1=10: A = A - M 00110 10101 0 ASR 00011 01010 1 2 Q0Q-1=01: A = A + M 11101 01010 1 ASR 11110 10101 0 3 Q0Q-1=10: A = A - M 00100 10101 0 ASR 00010 01010 1 4 Q0Q-1=01: A = A + M 11100 01010 1 ASR 11110 00101 0 5 Q0Q-1=10: A = A - M 00100 00101 0 ASR 00010 00010 1 ``` Result in A,Q = 00010 00010 = 66. **Answer: -6 × -11 = 66** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For M = -6 = 11010, -M is A. 00101 B. 00110 C. 11010 D. 11001 Answer: B. 2's complement of 11010 is 00110. (Key point: -M value) 2. Multiplier -11 = 10101 alternates bits. What does Booth do? A. Skip all steps B. Only shift C. Subtract or add at almost every step D. Add only Answer: C. Alternating 1s and 0s give 10 and 01 pairs often, so arithmetic is done in most steps. (Key point: Alternating multiplier) 3. What is -6 x -11? A. 66 = 00010 00010 B. -66 = 11101 11110 C. 66 = 00100 00100 D. 6 = 00000 00110 Answer: A. Both negative, product positive: A:Q = 00010 00010 = 66. (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 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× ## 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×