--- title: "Booth multiplication of -6 × 12" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:booth-6x12" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/booth-6x12 site: BCT Engineering --- # Booth multiplication of -6 × 12 Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2072 Kartik, 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-6x12 - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Multiply -6 × 12 using Booth's algorithm. ## Short answer Use 5-bit Booth: M=-6=11010, Q=12=01100. Sequence: 00 no change, 00 no change, 10 A=A−M, 11 no change, 01 A=A+M, each followed by ASR. Final A,Q = 11101 11000 = -72. ## Answer Use Booth's algorithm: 10 → A = A − M, 01 → A = A + M, 00/11 → no change, then ASR of A, Q, Q-1 for n cycles. Both numbers fit in 5 bits (−6 = 11010, 12 = 01100). Multiplicand M = -6 = 11010, multiplier Q = 12 = 01100, -M = 00110, n = 5 bits. ```text Step Action A Q Q-1 - Initial 00000 01100 0 1 Q0Q-1=00: no change 00000 01100 0 ASR 00000 00110 0 2 Q0Q-1=00: no change 00000 00110 0 ASR 00000 00011 0 3 Q0Q-1=10: A = A - M 00110 00011 0 ASR 00011 00001 1 4 Q0Q-1=11: no change 00011 00001 1 ASR 00001 10000 1 5 Q0Q-1=01: A = A + M 11011 10000 1 ASR 11101 11000 0 ``` Result in A,Q = 11101 11000 = -72. **Answer: -6 × 12 = -72** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In Booth's algorithm, what is done when (Q0, Q-1) = 01? A. A = A - M B. No change C. A = A + M D. Clear A Answer: C. 01 marks the end of a run of 1s, so M is added to A. (Key point: Booth pair 01) 2. For M = -6 = 11010 (5 bits), what is -M used for subtraction? A. 00110 B. 00101 C. 11101 D. 10110 Answer: A. -M is the 2's complement of 11010, which is 00110 (= +6). (Key point: Two's complement of M) 3. What is -6 x 12 and its A:Q form? A. 72 = 00010 01000 B. -72 = 11101 11000 C. -72 = 00010 01000 D. -60 = 11110 00100 Answer: B. After 5 cycles A:Q = 11101 11000 = -72. (Key point: Result) ## 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 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× - [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×