Octal to Hexadecimal Converter
Convert octal numbers to hexadecimal with step-by-step explanations and examples.
8
16
8
Octal to Hexadecimal Converter
Octal (Base-8)
Valid characters: 01234567
Hexadecimal (Base-16)
Result will appear here
Octal to Hexadecimal Conversion
Conversion Method:
Octal to Hexadecimal: Via binary conversion (octal→binary→hex)
Process:
- Convert each octal digit to 3 binary digits
- Group the combined binary digits into groups of 4
- Convert each 4-bit group to hexadecimal
Examples with Step-by-Step Solutions
Octal ↔ Hexadecimal Reference
Common conversions via binary intermediate
Octal → Binary → Hex
1₈→001₂→1₁₆
2₈→010₂→2₁₆
3₈→011₂→3₁₆
4₈→100₂→4₁₆
5₈→101₂→5₁₆
6₈→110₂→6₁₆
7₈→111₂→7₁₆
10₈→001000₂→8₁₆
12₈→001010₂→A₁₆
17₈→001111₂→F₁₆
Hex → Binary → Octal
1₁₆→0001₂→1₈
2₁₆→0010₂→2₈
3₁₆→0011₂→3₈
4₁₆→0100₂→4₈
5₁₆→0101₂→5₈
6₁₆→0110₂→6₈
7₁₆→0111₂→7₈
8₁₆→1000₂→10₈
A₁₆→1010₂→12₈
F₁₆→1111₂→17₈
Example 1:
(123)8
=
(53)16
Step-by-Step Solution:
Converting 123₍8₎ to base 16:
Step 1: Convert octal to binary first
(Each octal digit = 3 binary digits)
1₈ = 001₂
2₈ = 010₂
3₈ = 011₂
Combined binary: 001010011
Step 2: Group binary digits in groups of 4 for hexadecimal
Pad with leading zeros: 001010011 → 000001010011
Grouped: 0000 | 0101 | 0011
0000₂ = 0₁₀ = 0₁₆
0101₂ = 5₁₀ = 5₁₆
0011₂ = 3₁₀ = 3₁₆
Therefore: 123₈ = 053₁₆
Example 2:
(777)8
=
(1FF)16
Step-by-Step Solution:
Converting 777₍8₎ to base 16:
Step 1: Convert octal to binary first
(Each octal digit = 3 binary digits)
7₈ = 111₂
7₈ = 111₂
7₈ = 111₂
Combined binary: 111111111
Step 2: Group binary digits in groups of 4 for hexadecimal
Pad with leading zeros: 111111111 → 000111111111
Grouped: 0001 | 1111 | 1111
0001₂ = 1₁₀ = 1₁₆
1111₂ = 15₁₀ = F₁₆
1111₂ = 15₁₀ = F₁₆
Therefore: 777₈ = 1FF₁₆
Example 3:
(456)8
=
(12E)16
Step-by-Step Solution:
Converting 456₍8₎ to base 16:
Step 1: Convert octal to binary first
(Each octal digit = 3 binary digits)
4₈ = 100₂
5₈ = 101₂
6₈ = 110₂
Combined binary: 100101110
Step 2: Group binary digits in groups of 4 for hexadecimal
Pad with leading zeros: 100101110 → 000100101110
Grouped: 0001 | 0010 | 1110
0001₂ = 1₁₀ = 1₁₆
0010₂ = 2₁₀ = 2₁₆
1110₂ = 14₁₀ = E₁₆
Therefore: 456₈ = 12E₁₆
Example 4:
(234)8
=
(9C)16
Step-by-Step Solution:
Converting 234₍8₎ to base 16:
Step 1: Convert octal to binary first
(Each octal digit = 3 binary digits)
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
Combined binary: 010011100
Step 2: Group binary digits in groups of 4 for hexadecimal
Pad with leading zeros: 010011100 → 000010011100
Grouped: 0000 | 1001 | 1100
0000₂ = 0₁₀ = 0₁₆
1001₂ = 9₁₀ = 9₁₆
1100₂ = 12₁₀ = C₁₆
Therefore: 234₈ = 09C₁₆