Convert (11001001)excess-3 to octal

Short answer

Excess-3 code 11001001 splits into 1100 (12 - 3 = 9) and 1001 (9 - 3 = 6), giving decimal 96. Decimal 96 converts to octal 140.

Convert (11001001)excess-3 = (?)₈.

Decode the excess-3 groups to decimal (subtract 3 from each group), then convert decimal to octal.

Step 1: XS-3 to decimal

XS-3 group	1100	1001
Value	12	9
Minus 3	9	6

So the number is $96_{10}$ .

Step 2: Decimal to octal

Bottom to top: 140. Check: $1 \times 64 + 4 \times 8 + 0 = 96$ .

Answer: $(11001001)_{XS\text{-}3} = (96)_{10} = (140)_8$

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions