Hexadecimal to Binary Converter
Convert hexadecimal numbers to binary with step-by-step explanations and examples.
16
01
16
Hexadecimal to Binary Converter
Hexadecimal (Base-16)
Valid characters: 0123456789ABCDEF
Binary (Base-2)
Result will appear here
Hexadecimal to Binary Conversion
Conversion Method:
Hexadecimal to Binary: Direct expansion method (each digit to 4 binary)
Process:
- Convert each hex digit to its 4-digit binary equivalent
- Combine all binary groups
- Remove leading zeros if necessary
Examples with Step-by-Step Solutions
Hexadecimal to Binary Conversion Table
Each hexadecimal digit converts to 4 binary digits
0₁₆
↓
0000₂
1₁₆
↓
0001₂
2₁₆
↓
0010₂
3₁₆
↓
0011₂
4₁₆
↓
0100₂
5₁₆
↓
0101₂
6₁₆
↓
0110₂
7₁₆
↓
0111₂
8₁₆
↓
1000₂
9₁₆
↓
1001₂
A₁₆
↓
1010₂
B₁₆
↓
1011₂
C₁₆
↓
1100₂
D₁₆
↓
1101₂
E₁₆
↓
1110₂
F₁₆
↓
1111₂
Example 1:
(A)16
=
(1010)2
Step-by-Step Solution:
Converting A₍16₎ to base 2:
Step 1: Convert each hexadecimal digit to 4 binary digits
(Since 16 = 2⁴, each hex digit = 4 binary digits)
A₁₆ = 10₁₀ = 1×2^3 + 0×2^2 + 1×2^1 + 0×2^0 = 1010₂
Step 2: Combine all binary groups:
1010 = 1010
Therefore: A₁₆ = 1010₂
Example 2:
(FF)16
=
(11111111)2
Step-by-Step Solution:
Converting FF₍16₎ to base 2:
Step 1: Convert each hexadecimal digit to 4 binary digits
(Since 16 = 2⁴, each hex digit = 4 binary digits)
F₁₆ = 15₁₀ = 1×2^3 + 1×2^2 + 1×2^1 + 1×2^0 = 1111₂
F₁₆ = 15₁₀ = 1×2^3 + 1×2^2 + 1×2^1 + 1×2^0 = 1111₂
Step 2: Combine all binary groups:
1111 | 1111 = 11111111
Therefore: FF₁₆ = 11111111₂
Example 3:
(ABC)16
=
(101010111100)2
Step-by-Step Solution:
Converting ABC₍16₎ to base 2:
Step 1: Convert each hexadecimal digit to 4 binary digits
(Since 16 = 2⁴, each hex digit = 4 binary digits)
A₁₆ = 10₁₀ = 1×2^3 + 0×2^2 + 1×2^1 + 0×2^0 = 1010₂
B₁₆ = 11₁₀ = 1×2^3 + 0×2^2 + 1×2^1 + 1×2^0 = 1011₂
C₁₆ = 12₁₀ = 1×2^3 + 1×2^2 + 0×2^1 + 0×2^0 = 1100₂
Step 2: Combine all binary groups:
1010 | 1011 | 1100 = 101010111100
Therefore: ABC₁₆ = 101010111100₂
Example 4:
(123)16
=
(100100011)2
Step-by-Step Solution:
Converting 123₍16₎ to base 2:
Step 1: Convert each hexadecimal digit to 4 binary digits
(Since 16 = 2⁴, each hex digit = 4 binary digits)
1₁₆ = 1₁₀ = 0×2^3 + 0×2^2 + 0×2^1 + 1×2^0 = 0001₂
2₁₆ = 2₁₀ = 0×2^3 + 0×2^2 + 1×2^1 + 0×2^0 = 0010₂
3₁₆ = 3₁₀ = 0×2^3 + 0×2^2 + 1×2^1 + 1×2^0 = 0011₂
Step 2: Combine all binary groups:
0001 | 0010 | 0011 = 000100100011
Remove leading zeros: 100100011
Therefore: 123₁₆ = 100100011₂