This subscript denotes the “base” of the number. Binary is a base-two system, octal is base-eight.
Original Binary: 10011011 Grouping: 10 011 011 Adding Zeros for Groups of Three: 010 011 011[1] X Research source
010 011 011421 421 421 001421 110 010 001421 421 421 Note, if you’re looking for a shortcut, you can skip this step and just compare your sets of binary numbers to this octal conversion chart.
Problem: Convert 1010100112 to octal. Separate into threes: 101 010 011 Add placeholders: 101 010 011421 421 421 Mark each places: 101 010 011421 421 421401 020 021[2] X Research source
Convert 1010100112 to octal.
101 010 011
101 010 011421 421 421
101 010 011421 421 421401 020 021[2] X Research source
Problem: Convert 1010100112 to octal. Separate, add placeholders, and mark each place: 101 010 011421 421 421401 020 021 Add up each set of three: (4+0+1)(0+2+0)(0+2+1)=5,2,3{\displaystyle (4+0+1)(0+2+0)(0+2+1)=5,2,3}
Problem: Convert 1010100112 to octal. Separate, add placeholders, and mark each place: 101 010 011421 421 421401 020 021 Add up each set of three: (4+0+1)(0+2+0)(0+2+1)=5,2,3{\displaystyle (4+0+1)(0+2+0)(0+2+1)=5,2,3}
Convert 1010100112 to octal.
101 010 011421 421 421401 020 021
(4+0+1)(0+2+0)(0+2+1)=5,2,3{\displaystyle (4+0+1)(0+2+0)(0+2+1)=5,2,3}
Problem: Convert 1010100112 to octal. Separate, add placeholders, mark places, and add totals: 101 010 011 5 — 2 — 3 Put converted numbers back together: 523
Convert 1010100112 to octal.
101 010 011 5 — 2 — 3
523
Problem: Convert 1010100112 to octal. Conversion: 523. Final Answer: 5238[3] X Research source
Convert 1010100112 to octal.
523.
5238[3] X Research source
Note how numbers 8 and 9 don’t have straight conversions. In octal, these numbers do not exist, since there are only 8 digits (0-7) in a base-eight system.
101. 1 → 101 . 100 1. 01001 → 001 . 010 010 1001101. 0101 → 001 001 101 . 010 100
0 → 000 1 → 001 2 → 010 3 → 011 4 → 100 5 → 101 6 → 110 7 → 111[5] X Research source
