--- title: "Booth multiplication of 10 × (-5)" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:booth-10x-5" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/booth-10x-5 site: BCT Engineering --- # Booth multiplication of 10 × (-5) Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2076 Chaitra, 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-10x-5 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Multiply 10 × (-5) using Booth's multiplication algorithm. ## Short answer Using Booth multiplication with 5-bit operands, process multiplier bit pairs and arithmetic-shift right after each add or subtract. For 10 times -5, the final A:Q is 1111001110, which equals -50. ## Answer Booth's algorithm with 5-bit registers (10 = 01010, −5 = 11011). Multiplicand M = 10 = 01010, multiplier Q = -5 = 11011, -M = 10110, n = 5 bits. ```text Step Action A Q Q-1 - Initial 00000 11011 0 1 Q0Q-1=10: A = A - M 10110 11011 0 ASR 11011 01101 1 2 Q0Q-1=11: no change 11011 01101 1 ASR 11101 10110 1 3 Q0Q-1=01: A = A + M 00111 10110 1 ASR 00011 11011 0 4 Q0Q-1=10: A = A - M 11001 11011 0 ASR 11100 11101 1 5 Q0Q-1=11: no change 11100 11101 1 ASR 11110 01110 1 ``` Result in A,Q = 11110 01110 = -50. **Answer: 10 × -5 = -50** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For M = 10 = 01010, -M is A. 10110 B. 10101 C. 01010 D. 11010 Answer: A. 2's complement of 01010 is 10110. (Key point: -M value) 2. What is -5 in 5-bit 2's complement? A. 10101 B. 11011 C. 10011 D. 11010 Answer: B. 5 = 00101; invert 11010 and add 1 = 11011. (Key point: Multiplier -5) 3. What is 10 x -5 and its form? A. 50 = 00001 10010 B. -50 = 00001 10010 C. -50 = 11110 01110 D. -5 = 11111 11011 Answer: C. A:Q = 11110 01110 = -50. (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 -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×