🔄 One's Complement Calculator
Calculate one's complement of binary numbers
How to Use This Calculator
Enter Binary Number
Input the binary number for which you want to calculate the one's complement. The calculator accepts only 0s and 1s. Examples: 1010, 1100, 1111. One's complement is found by flipping all bits (0 becomes 1, 1 becomes 0).
Click Calculate One's Complement
Press the "Calculate One's Complement" button to perform the operation. The calculator will flip each bit of the input binary number and display the result.
Review Results
The result shows the one's complement in binary format and its decimal equivalent. You'll also see a step-by-step breakdown showing how each bit was flipped.
Formula
One's Complement = Flip all bits (0 → 1, 1 → 0)
For n-bit number: One's Complement = (2^n - 1) - Original
How it works:
One's complement is calculated by inverting (flipping) all bits in the binary representation. Every 0 becomes 1, and every 1 becomes 0. This is the simplest method for representing negative numbers in binary, though it's less commonly used than two's complement today.
One's Complement Properties:
- One's complement of a number x in n bits = (2^n - 1) - x
- For 8-bit numbers: range is -127 to +127 (or 0 to 255 for unsigned)
- Has two representations for zero: +0 (00000000) and -0 (11111111)
- Adding a number and its one's complement gives all 1s
Example 1: One's Complement of 1010 (10 in decimal)
Original: 1010
Flip all bits:
Position 0: 0 → 1
Position 1: 1 → 0
Position 2: 0 → 1
Position 3: 1 → 0
Result: 0101 (binary) = 5 (decimal)
Note: 10 + 5 = 15 = 1111 (all 1s) ✓
Example 2: One's Complement of 1111 (15 in decimal)
Original: 1111
Flip all bits: 0000
Result: 0000 (binary) = 0 (decimal)
Note: 15 + 0 = 15 = 1111 (all 1s) ✓
Example 3: One's Complement for Negative Numbers
In one's complement system:
+5 = 0101
-5 = 1010 (one's complement of 0101)
+5 + (-5) = 0101 + 1010 = 1111 (all 1s, which is -0)
Frequently Asked Questions
What is one's complement?
One's complement is a method of representing negative numbers in binary by inverting all bits. To get the one's complement of a number, simply flip all its bits: 0 becomes 1, and 1 becomes 0. It's one of the earliest methods for representing signed integers in computers.
What's the difference between one's complement and two's complement?
One's complement flips all bits. Two's complement flips all bits and then adds 1. Two's complement is more commonly used today because: it has only one representation for zero (no +0 and -0), arithmetic is simpler, and it's the standard in modern computers.
Why does one's complement have two zeros?
In one's complement, +0 is represented as 00000000 and -0 is represented as 11111111. This is because flipping all bits of 0 gives all 1s. This dual representation of zero is one reason why two's complement (which has only one zero) is preferred in modern computing.
How is one's complement used today?
One's complement is rarely used in modern computers for representing signed integers, as two's complement is the standard. However, it's still used in: checksum calculations (like TCP/IP), error detection, some older computer architectures, and educational contexts to understand binary number systems.
What happens when you add a number and its one's complement?
Adding a number and its one's complement always results in all 1s (for the bit length of the number). For example, 1010 + 0101 = 1111. This property is useful in checksum calculations and error detection.
Can I use one's complement with decimal numbers?
Yes, but the calculator converts the decimal number to binary first. The one's complement is calculated by flipping all bits, then converted back to decimal. Enter your decimal number, and the calculator will show both binary and decimal representations.