--- title: "Signed division and non-restoring division" subject: "Computer Organization and Architecture" chapter: 5 key: "semester_5/computer_organization_and_architecture:nonrestoring-division" source: https://www.bctengineer.com/q/semester_5/computer_organization_and_architecture/nonrestoring-division site: BCT Engineering --- # Signed division and non-restoring division Computer Organization and Architecture · Chapter 5: Computer Arithmetic - Asked in: 2073 Shrawan, 8 marks - Video: [Non Restoring Division Algorithm: Flowchart and Example | COA](https://www.youtube.com/watch?v=je7RSR6w37c) — Engineering Funda - 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/nonrestoring-division - Whole chapter: https://www.bctengineer.com/md/semester_5/computer_organization_and_architecture/chapter-5 ## Question Explain the signed binary division algorithm. Use the non-restoring division algorithm to divide 15 by 4. ## Short answer Signed division: signs are handled separately; quotient sign = Sd XOR Sv, remainder sign = sign of dividend. Magnitudes are divided non-restoringly. For 15÷4, with n=4, Q=1111, M=00100, the non-restoring algorithm yields quotient=3 (0011), remainder=3 (00011). ## Answer #### Signed binary division Division of signed integers is done on the magnitudes (sign-magnitude method), and the signs are handled separately: 1. Store the sign of the dividend (Sd) and of the divisor (Sv), and take the absolute values. 2. Divide the magnitudes with the restoring or non-restoring algorithm to get the quotient Q and remainder R. 3. **Quotient sign** = Sd XOR Sv (negative if the signs differ). 4. **Remainder sign** = sign of the dividend, so that dividend = divisor × quotient + remainder. 5. If the dividend and divisor are in 2's complement, convert negative values to positive before step 2 and convert the results back at the end. 6. Check for divide overflow: the divisor must not be 0, and the quotient must fit in the register. #### Non-restoring algorithm 1. Load A = 0, Q = dividend, M = divisor, SC = n. 2. If the sign of A is 0 (A ≥ 0): shift A,Q left, then A = A − M. If the sign of A is 1 (A < 0): shift A,Q left, then A = A + M. 3. If the new A is non-negative, set Q0 = 1; otherwise set Q0 = 0. 4. SC = SC − 1. Repeat from step 2 until SC = 0. 5. If A < 0 at the end, correct the remainder: A = A + M. 6. Q is the quotient and A is the remainder. #### 15 ÷ 4 Both numbers are positive, so no sign handling is needed. Q = 15 = 1111, M = 4 = 00100 (A and M have n + 1 = 5 bits), n = 4. ```text Step Action A Q - Initial 00000 1111 1 Shift left A,Q 00001 1110 A>=0 before shift: A = A - M (=-3) 11101 1110 (Q0=0) 2 Shift left A,Q 11011 1100 A<0 before shift: A = A + M (=-1) 11111 1100 (Q0=0) 3 Shift left A,Q 11111 1000 A<0 before shift: A = A + M (=3) 00011 1001 (Q0=1) 4 Shift left A,Q 00111 0010 A>=0 before shift: A = A - M (=3) 00011 0011 (Q0=1) ``` The final A is positive, so no remainder correction is needed. **Answer: 15 ÷ 4: quotient = 3 (0011), remainder = 3 (00011)** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In sign-magnitude signed division, the quotient sign is: A. Sign of dividend XOR sign of divisor B. Sign of divisor C. Always positive D. Sign of dividend AND divisor Answer: A. The quotient is negative when the signs differ. (Key point: Signed division sign rules) 2. The remainder takes the sign of: A. The dividend B. The divisor C. The quotient D. Always positive Answer: A. So that dividend = divisor x quotient + remainder. (Key point: Remainder sign) 3. What divide-overflow checks are made? A. Divisor not 0 and quotient fits in the register B. Dividend not 0 C. Both operands equal D. Remainder is zero Answer: A. Divide by zero or a too-large quotient must be flagged. (Key point: Overflow check) 4. If A >= 0 before the shift in non-restoring division: A. Shift left then A = A - M B. Shift left then A = A + M C. Restore D. Add M without shift Answer: A. Negative A uses A + M. (Key point: Non-restoring rule) 5. 15 / 4 gives: A. Quotient 3, remainder 3 B. Quotient 4, remainder 0 C. Quotient 3, remainder 1 D. Quotient 2, remainder 7 Answer: A. 4 x 3 + 3 = 15; final A = 3 is positive. 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