8’s complement of the octal number (7650) is –

Key concept: For an n-digit number N in a radix-r system (radix 8 here, i.e. octal), the r's complement is defined as rn − N. In practice it is computed by first taking the (r−1)'s complement of each digit — subtracting the digit from (r−1) — and then adding 1 to the result.

1. Take the octal digits of 7650: 7, 6, 5, 0. Compute the 7's complement of each digit (i.e., 7 − digit, since r − 1 = 7 for octal): 7 − 7 = 0, 7 − 6 = 1, 7 − 5 = 2, 7 − 0 = 7, giving 0127.

2. Add 1 to 0127 in base 8: the last digit 7 + 1 = 8 (decimal) = 10 in octal, so write 0 and carry 1; the carry added to the next digit gives 2 + 1 = 3; the remaining digits stay unchanged. Result: 0130.

Cross-check: For any n-digit number N, N plus its r's complement must equal rn. Adding 7650 and 0130 digit-by-digit in base 8: 0+0=0; 5+3=8 → write 0, carry 1; 6+1+carry 1=8 → write 0, carry 1; 7+0+carry 1=8 → write 0, carry 1; the final carry gives a leading 1. The sum is 10000 (base 8), which equals 84, confirming that 0130 is indeed the correct 8's complement.

Answer: 0130 (octal).