--- title: "Booth multiplication of -7 × -10" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:booth-7x-10" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/booth-7x-10 site: BCT Engineering --- # Booth multiplication of -7 × -10 Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2078 Kartik, 4 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-7x-10 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Multiply -7 × -10 using Booth's multiplication algorithm. ## Short answer In Booth multiplication, add or subtract the multiplicand based on multiplier bit pair Q0,Q-1 and arithmetic-shift right each cycle. For -7 times -10, the final A:Q is 0001000110, which equals 70. ## Answer Booth's algorithm with 5-bit registers (−7 = 11001, −10 = 10110). Multiplicand M = -7 = 11001, multiplier Q = -10 = 10110, -M = 00111, n = 5 bits. ```text Step Action A Q Q-1 - Initial 00000 10110 0 1 Q0Q-1=00: no change 00000 10110 0 ASR 00000 01011 0 2 Q0Q-1=10: A = A - M 00111 01011 0 ASR 00011 10101 1 3 Q0Q-1=11: no change 00011 10101 1 ASR 00001 11010 1 4 Q0Q-1=01: A = A + M 11010 11010 1 ASR 11101 01101 0 5 Q0Q-1=10: A = A - M 00100 01101 0 ASR 00010 00110 1 ``` Result in A,Q = 00010 00110 = 70. **Answer: -7 × -10 = 70** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Multiplier -10 = 10110 starts with Q0 Q-1 = 00. What happens at step 1? A. No arithmetic, just ASR B. A = A - M C. A = A + M D. Stop Answer: A. Pair 00 means no add or subtract; only the shift. (Key point: Start of Booth) 2. For M = -7 = 11001, -M is A. 00110 B. 11000 C. 00111 D. 10111 Answer: C. 2's complement of 11001 is 00111 (+7). (Key point: -M value) 3. What is -7 x -10? A. -70 = 11101 11010 B. 70 = 00010 00110 C. 70 = 00100 01100 D. 7 = 00000 00111 Answer: B. Negative x negative gives +70; A:Q = 00010 00110. (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 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×