1’s Complement
- Definition: The 1’s complement of a binary number is created by flipping all the bits (i.e., converting 0s to 1s and 1s to 0s).
- Example: Consider an 8-bit number: Original: 00010110 (which equals +22 in decimal)
1’s complement: 11101001 (this denotes -22 in 1’s complement)
- Key Characteristics: It generates a mirrored representation of the number. To perform subtraction on a number, you may add its 1’s complement followed by an addition of 1 (although this process is more intuitively managed using 2’s complement). There exist two forms of zero: Positive zero: 00000000 Negative zero: 11111111
One’s Complement of a Binary Number
In simple words, if we want to understand the One’s complement, so one’s complement is toggling or exchanging all the 0’s into 1 and all the 1’s into 0 of any number. Suppose there is a binary number 11001001, then its one’s complement will be 00110110.
In actuality, the one’s complement means the addition of a negative integer to the number, and this eliminates the requirement of a separate subtraction processor.
How to Find One’s Complement of a Number?
To find one’s complement of any number, follow the below steps:
- Convert the number of any number system to a binary number system, i.e. if the number is in octal, decimal, hexadecimal, or any other number system; so convert it into a binary number system. If there is a number 10 and we need to find its one complement convert it into a binary number system, i.e. 1010.
- After, having the number in binary form. Now, invert or exchange all the 0’s to 1 and all the 1’s to 0. Like, 1010 will be 0101.
- The resulting binary number is the 1’s complement of the given number.
CASE
If the decimal number was a negative number, suppose we have a number say -10. To find out 1’s complement of such number. Follow the given steps:
- Convert the number into the binary number system as we do for the positive number.
- Now, exchange all the 1’s to 0 and 0’s to 1.
- Take the transpose of the negative binary number.
2’s Complement
Definition: The 2’s complement is derived by first calculating the 1’s complement of a binary number and subsequently adding 1 to the least significant bit (LSB).
- Example: Using the identical number: 00010110 (+22) 1’s complement: 11101001 Add 1: 11101010 → This represents -22 in 2’s complement.
- Key Characteristics: It is the predominant technique employed in computers for representing signed integers. There is a single representation for zero: 00000000 Facilitates binary addition and subtraction — eliminating the necessity for distinct subtraction logic.
The range for an 8-bit number: Signed integers: −128 to +127, Unsigned integers: 0 to 255
- Summary Overview
Operation | 1’s Complement | 2’s Complement |
| How to find | Invert all bits | Invert all bits + Add 1 |
| Zero representations | Two (positive and negative) | One (positive only) |
| Arithmetic ease | Complex (requires end-around carry) | Simple and direct |
| Commonly used? | No (historical interest) | Yes (used in modern systems) |
One’s Complement of a Binary Number
In simple words, if we want to understand the One’s complement, so one’s complement is toggling or exchanging all the 0’s into 1 and all the 1’s into 0 of any number. Suppose there is a binary number 11001001, then its one’s complement will be 00110110.
In actuality, the one’s complement means the addition of a negative integer to the number, and this eliminates the requirement of a separate subtraction processor.
How to Find One’s Complement of a Number?
To find one’s complement of any number, follow the steps below:
- Convert the number of any number system to a binary number system, i.e. if the number is in octal, decimal, hexadecimal, or any other number system; so convert it into a binary number system. If there is a number 10 and we need to find its one complement convert it into a binary number system, i.e. 1010.
- After having the number in binary form. Now, invert or exchange all the 0’s to 1 and all the 1’s to 0. Like, 1010 will be 0101.
- The resulting binary number is the 1’s complement of the given number.
CASE
If the decimal number was a negative number, suppose we have a number say -10. To find out 1’s complement of such number. Follow the given steps:
- Convert the number into the binary number system as we do for the positive number.
- Now, exchange all the 1’s to 0 and 0’s to 1.
- Take the transpose of the negative binary number.
