One's Complement Calculator

Convert between decimal and one's complement binary representation

One's Complement Calculator

Number of bits for binary representation

Example One's Complement Conversions

Positive Numbers (8-bit)

7 → One's Complement
0000 0111 → 1111 1000
Represents -7
15 → One's Complement
0000 1111 → 1111 0000
Represents -15

Binary to Decimal (8-bit)

1111 1000 → Decimal
Flip bits: 0000 0111 = 7
Result: -7
0101 0101 → Decimal
Positive: 85
Result: 85

One's Complement Rules

Sign Bit

  • • First bit = 0: Positive number
  • • First bit = 1: Negative number

Conversion Process

  • • Positive: Flip all bits
  • • Negative: Flip all bits to get magnitude
  • • All bits are inverted (0↔1)

Range (n-bit)

  • • Positive: 0 to 2^(n-1) - 1
  • • Negative: -(2^(n-1) - 1) to -0
  • • Two representations for zero

Bit Width Ranges

4-bit
Range: -7 to +7
8-bit
Range: -127 to +127
16-bit
Range: -32,767 to +32,767
32-bit
Range: -2,147,483,647 to +2,147,483,647

One's Complement Tips

Simple bit flipping operation

Two representations for zero

Less common than two's complement

Used in some legacy systems

Understanding One's Complement

What is One's Complement?

One's complement is a mathematical operation on binary numbers that flips all bits - changing every 0 to 1 and every 1 to 0. It's one method used to represent negative numbers in binary systems, though it's less common than two's complement.

Key Characteristics:

  • • Simple bit inversion operation
  • • Sign bit determines positive/negative
  • • Two representations for zero (+0 and -0)
  • • Symmetric range around zero
  • • End-around carry in arithmetic

Applications and Limitations

Historical Use

One's complement was used in some early computer systems and is still found in certain specialized applications and legacy systems.

Limitations

The main limitation is having two representations for zero (0000 and 1111 in 4-bit), which complicates arithmetic operations and comparisons.

vs Two's Complement

Two's complement (one's complement + 1) is more widely used in modern systems because it has only one representation for zero and simpler arithmetic.