One's Complement Calculator – Binary Number Representation
Convert numbers to one's complement binary representation.
Table of Contents
How to Use
- Select input type: decimal or binary
- Choose the bit width (4, 8, 16, or 32 bits)
- Enter your number value
- Click calculate to see the one's complement representation
- View the binary result and decimal equivalent
What is One's Complement?
One's complement is a method of representing signed integers in binary. In this system, negative numbers are represented by inverting all the bits of the corresponding positive number (changing 0s to 1s and 1s to 0s).
For example, in 8-bit one's complement, +5 is 00000101, and -5 is 11111010 (all bits flipped).
How One's Complement Works
The one's complement system uses the most significant bit (MSB) as the sign bit:
- MSB = 0: The number is positive
- MSB = 1: The number is negative
- To negate a number, flip all bits
- Zero has two representations: +0 (all 0s) and -0 (all 1s)
Range of Values
For an n-bit one's complement number, the range is:
- 4 bits: -7 to +7
- 8 bits: -127 to +127
- 16 bits: -32,767 to +32,767
- 32 bits: -2,147,483,647 to +2,147,483,647
Note that the range is symmetric around zero, unlike two's complement.
One's Complement vs Two's Complement
One's complement has some disadvantages compared to two's complement:
- Two representations of zero (+0 and -0)
- Addition requires end-around carry
- Modern computers typically use two's complement instead
- One's complement was used in older computer systems
Frequently Asked Questions
- Why does one's complement have two zeros?
- In one's complement, +0 is represented as all 0s (e.g., 00000000), and -0 is represented as all 1s (e.g., 11111111). This is because flipping all bits of +0 gives -0. This dual representation is one reason two's complement is preferred in modern systems.
- How do I convert a negative decimal to one's complement?
- First, convert the absolute value to binary. Then, flip all the bits (change 0s to 1s and 1s to 0s). The result is the one's complement representation of the negative number.
- What is end-around carry?
- When adding one's complement numbers, if there's a carry out of the most significant bit, it must be added back to the least significant bit. This is called end-around carry and is necessary for correct arithmetic in one's complement.
- Is one's complement still used today?
- One's complement is rarely used in modern computers for integer arithmetic. However, it's still used in some applications like IP header checksums. Two's complement is the standard for signed integer representation in modern systems.