Hexadecimal to Octal Converter
Convert hexadecimal numbers to octal with step-by-step explanations and examples.
16
8
16
Hexadecimal to Octal Converter
Hexadecimal (Base-16)
Valid characters: 0123456789ABCDEF
Octal (Base-8)
Result will appear here
Hexadecimal to Octal Conversion
Conversion Method:
Hexadecimal to Octal: Via binary conversion (hex→binary→octal)
Process:
- Convert each hex digit to 4 binary digits
- Group the combined binary digits into groups of 3
- Convert each 3-bit group to octal
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:
(FF)16
=
(377)8
Step-by-Step Solution:
Converting FF₍16₎ to base 8:
Step 1: Convert hexadecimal to binary first
(Each hex digit = 4 binary digits)
F₁₆ = 1111₂
F₁₆ = 1111₂
Combined binary: 11111111
Step 2: Group binary digits in groups of 3 for octal
Pad with leading zeros: 11111111 → 011111111
Grouped: 011 | 111 | 111
011₂ = 3₁₀ = 3₈
111₂ = 7₁₀ = 7₈
111₂ = 7₁₀ = 7₈
Therefore: FF₁₆ = 377₈
Example 2:
(ABC)16
=
(5274)8
Step-by-Step Solution:
Converting ABC₍16₎ to base 8:
Step 1: Convert hexadecimal to binary first
(Each hex digit = 4 binary digits)
A₁₆ = 1010₂
B₁₆ = 1011₂
C₁₆ = 1100₂
Combined binary: 101010111100
Step 2: Group binary digits in groups of 3 for octal
Grouped: 101 | 010 | 111 | 100
101₂ = 5₁₀ = 5₈
010₂ = 2₁₀ = 2₈
111₂ = 7₁₀ = 7₈
100₂ = 4₁₀ = 4₈
Therefore: ABC₁₆ = 5274₈
Example 3:
(123)16
=
(443)8
Step-by-Step Solution:
Converting 123₍16₎ to base 8:
Step 1: Convert hexadecimal to binary first
(Each hex digit = 4 binary digits)
1₁₆ = 0001₂
2₁₆ = 0010₂
3₁₆ = 0011₂
Combined binary: 000100100011
Step 2: Group binary digits in groups of 3 for octal
Grouped: 000 | 100 | 100 | 011
000₂ = 0₁₀ = 0₈
100₂ = 4₁₀ = 4₈
100₂ = 4₁₀ = 4₈
011₂ = 3₁₀ = 3₈
Therefore: 123₁₆ = 0443₈
Example 4:
(DEF)16
=
(6757)8
Step-by-Step Solution:
Converting DEF₍16₎ to base 8:
Step 1: Convert hexadecimal to binary first
(Each hex digit = 4 binary digits)
D₁₆ = 1101₂
E₁₆ = 1110₂
F₁₆ = 1111₂
Combined binary: 110111101111
Step 2: Group binary digits in groups of 3 for octal
Grouped: 110 | 111 | 101 | 111
110₂ = 6₁₀ = 6₈
111₂ = 7₁₀ = 7₈
101₂ = 5₁₀ = 5₈
111₂ = 7₁₀ = 7₈
Therefore: DEF₁₆ = 6757₈