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Restoring division of 10 by 3

Short answer

Restoring division shifts A,Q left, subtracts divisor, and restores A if negative while setting quotient bits. For 10 divided by 3, the quotient is 3 (0011) and the remainder is 1 (00001).

Perform 10/3 using the restoring division algorithm.

Restoring division: shift left A,Q; A = A − M; if A < 0 restore and Q0 = 0, else Q0 = 1; repeat n times.

Dividend = 10 = 1010 (Q), divisor M = 3 = 00011 (n+1 = 5 bits), A = 0, n = 4.

Step  Action                  A      Q
-     Initial                 00000  1010
1     Shift left A,Q          00001  0100
      A = A - M (1 - 3 = -2)  11110  0100
      A<0: Q0=0, restore A    00001  0100
2     Shift left A,Q          00010  1000
      A = A - M (2 - 3 = -1)  11111  1000
      A<0: Q0=0, restore A    00010  1000
3     Shift left A,Q          00101  0000
      A = A - M (5 - 3 = 2)   00010  0000
      A>=0: Q0=1              00010  0001
4     Shift left A,Q          00100  0010
      A = A - M (4 - 3 = 1)   00001  0010
      A>=0: Q0=1              00001  0011

Answer: 10 ÷ 3: quotient = 3 (0011), remainder = 1 (00001)

✓ Answer checked by Claude Opus 5.5 (high effort)

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