18 min read

Octal and Hexadecimal — and Choosing a Route

Convert between octal and hex through binary, and choose the quickest method for any conversion.

Go Through Binary

There is no direct grouping trick between octal and hex, because 3 bits and 4 bits do not line up. The easy route is through binary : 1 Expand each digit into bits (3 for octal, 4 for hex). 2 Regroup the bits (4 for hex, 3 for octal) from the right, padding with leading zeros. 3 Change each new group into a digit.

Worked example

Convert 7352₈ to hexadecimal

Step 1 — octal to binary (3 bits each): Octal 7352 Bits 111011101010 Binary: 111011101010 (12 bits) Step 2 — regroup in fours from the right: Group 111011101010 Hex digit E E A Answer: 7352₈ = EEA₁₆

Worked example

Convert 1A5₁₆ to octal

Step 1 — hex to binary (4 bits each): Hex 1 A 5 Bits 000110100101 Binary: 000110100101 \to 110100101 (drop leading zeros) Step 2 — regroup in threes from the right: Group 110100101 Octal digit 645 Answer: 1A5₁₆ = 645₈

You could also go through decimal (octal \to decimal by place value, then decimal \to hex by division). It works, but it is longer and there are more chances to slip. Binary is usually faster.

Conversion methods — a summary to copy into your notes
Conversion methods — a summary to copy into your notes

Practice

What is the quickest reliable way to convert 3E8₁₆ to octal?

Go Through Binary

There is no direct grouping trick between octal and hex, because 3 bits and 4 bits do not line up. The easy route is through binary : 1 Expand each digit into bits (3 for octal, 4 for hex). 2 Regroup the bits (4 for hex, 3 for octal) from the right, padding with leading zeros. 3 Change each new group into a digit.

Worked example

Convert 7352₈ to hexadecimal

Step 1 — octal to binary (3 bits each): Octal 7352 Bits 111011101010 Binary: 111011101010 (12 bits) Step 2 — regroup in fours from the right: Group 111011101010 Hex digit E E A Answer: 7352₈ = EEA₁₆

Worked example

Convert 1A5₁₆ to octal

Step 1 — hex to binary (4 bits each): Hex 1 A 5 Bits 000110100101 Binary: 000110100101 \to 110100101 (drop leading zeros) Step 2 — regroup in threes from the right: Group 110100101 Octal digit 645 Answer: 1A5₁₆ = 645₈

You could also go through decimal (octal \to decimal by place value, then decimal \to hex by division). It works, but it is longer and there are more chances to slip. Binary is usually faster.

Which Method Should I Use?

Conversion methods — a summary to copy into your notes
Conversion methods — a summary to copy into your notes

Practice

What is the quickest reliable way to convert 3E8₁₆ to octal?