Binary to Decimal Converter
Convert binary (base-2) numbers to decimal (base-10) and vice versa. Supports big integers and optional signed two’s-complement interpretation.
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Number Conversion
Bit length: 4
Valid binary
Conversion Results
1011
11
Hexadecimal:
0xB
Octal:
0o13
Bit Length:
4 bits
Understanding Binary and Decimal
Binary (base-2) is a numeral system that uses only two digits: 0 and 1. Each digit is called a bit. Computers use binary because digital circuits have two stable states (on/off).
Decimal (base-10) is the standard numeral system using ten digits: 0-9. It’s the system humans use for everyday counting.
Conversion Examples
Binary to Decimal:
1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11₁₀
Decimal to Binary:
11₁₀ = 8 + 2 + 1 = 1011₂
Two’s Complement
Two’s complement is a mathematical operation on binary numbers used to represent signed integers. The most significant bit indicates the sign (0 for positive, 1 for negative).
Example (8-bit):
00001011₂ = 11₁₀ (positive)11110101₂ = -11₁₀ (negative)
Bit Distribution
Ones (1): 3 (75%)
Zeros (0): 1 (25%)
Bit Pattern Visualization
1
0
1
1
MSB
LSB
Total Bits:
4
Ones Count:
3
Zeros Count:
1
Common Binary Values
Binary
Decimal
Hex
0000
0
0x0
0001
1
0x1
0010
2
0x2
0100
4
0x4
1000
8
0x8
1111
15
0xF
11111111
255
0xFF