The 8's complement of the four-digit octal number (6100)8 is:

Concept

For an n-digit number N in base r, the radix complement is rn − N.

An equivalent digit method is to form the (r − 1)'s complement by replacing each digit d with r − 1 − d, and then add 1.

Application

1. Here r = 8 and n = 4, so use the 7's-complement-and-add-1 method for (6100)8.

2. Replace each digit d by 7 − d: 6 → 1, 1 → 6, 0 → 7, and 0 → 7. The 7's complement is therefore (1677)8.

3. Add one in base 8: (1677)8 + (0001)8 = (1700)8.

Cross-check

(6100)8 + (1700)8 = (10000)8 = 84, so the required 8's complement is (1700)8.