In digital electronics, the binary system is one of the most common number representation techniques. As its name suggest binary number system deals with only two number 0 and 1, this can be used by any device which is operating in two states. The binary number system has two complements 1's and 2's complement.
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.
Examples of One's Complement of a Binary Number
Here are examples of One's complement of a binary number for better understanding :
1. Evaluate the 1's complement of the 11010011.
Simply invert each bit of the number, and hence the 1's complement for the above binary number is - 00101100
2. Evaluate the 1's complement for the fractional binary number 00111.001.
The 1's complement representation of the fractional binary number will be 11000.110.
3. Evaluate 1's complement of all 4-bit binary numbers
| Number | Binary Representation | 1's complement |
|---|
| 0 | 0000 | 1111 |
| 1 | 0001 | 1110 |
| 2 | 0010 | 1101 |
| 3 | 0011 | 1100 |
| 4 | 0100 | 1011 |
| 5 | 0101 | 1010 |
| 6 | 0110 | 1001 |
| 7 | 0111 | 1000 |
| 8 | 1000 | 0111 |
| 9 | 1001 | 0110 |
| 10 | 1010 | 0101 |
| 11 | 1011 | 0100 |
| 12 | 1100 | 0011 |
| 13 | 1101 | 0010 |
| 14 | 1110 | 0001 |
| 15 | 1111 | 0000 |
1's Complement Representation in Signed Magnitude
In sign-magnitude, the leftmost bit indicates the sign of the integer. Representation of the positive remains the same. In sign-magnitude, 6 is a positive number, its binary representation is 0000 0110, and it will be represented as it is, i.e. 0000 0110. Whereas a negative number suppose -6 will be represented as 1111 1001. Negative integers are generated by reversing all the bits or by performing a bitwise complement of a positive integer.
Range of 1's Complement Number
For n bits register, the smallest negative number that can be stored is -(2(n-1)-1) and the largest positive largest number that can be stored is (2(n-1)-1).
NOTE: This (sign) representation has an ambiguous representation of the number 0. It has two different representations for 0; negative zero (-0) is 1 1111 in the five-bit register and the positive zero (+0) is 0 0000 in the five-bit register.
Uses of 1's Complement
- Represent Signed binary number: 1's complement is used to represent signed binary numbers, as positive signed binary numbers can be represented as it is, 1's complement is widely used to represent negative binary numbers in sign-magnitude.
- 1's complement is also used in various arithmetic binary operations like subtraction, addition, etc.
For more details, you can refer Difference between 1’s Complement representation and 2’s Complement representation Technique article.
Conclusion
In the conclusion, we discussed all the aspects of one's complement like definition, steps to be followed, significance, representation in sign magnitude, range, examples, uses, etc. One's complement of a binary number is the toggling or complement of the series in which it is given.
Similar Reads
Two's Complement
There are three different ways to represent signed integer (article). a: Signed bit, b: 1’s Complement, and c: 2’s Complement. Let’s try to understand how these methods have derived and why 2’s complement is preferred over others. As we know that data are stored in bits. How can we store signed inte
9 min read
Complement of Graph
Consider a set A and let U represent the universal set. The complement of set A is defined as:Ac = U - ABut what about graphs? A graph G ( V, E), which consists of a set of vertices V and edges E, can also have a complement. Is it possible to find the complement of a graph? The complement of a graph
4 min read
Functionally Complete Operations
Prerequisite - Functional Completeness A switching function is expressed by binary variables, the logic operation symbols, and constants 0 and 1. When every switching function can be expressed by means of operations in it, then only a set of operation is said to be functionally complete. The set (AN
3 min read
Functional Completeness in Digital Logic
Functional Completeness is a crucial concept in digital logic design. A set of logical operators is functionally complete if it can be used to express any Boolean function. This means that any logical operation, regardless of complexity, can be constructed using only operators from a functionally co
6 min read
Implementing Any Circuit Using NAND Gate Only
A universal gate is such a gate that we can implement any Boolean function, no matter how complex, using a circuit that consists of only that particular universal gate. The NAND & NOR gates are the most commonly encountered universal gates in digital logic.In this article, we will take a look at
8 min read
Arithmetic Operations of 2's Complement Number System
We all know how to perform arithmetic operations of binary number systems. However, computer system generally stores numbers in 2's complement format. So it becomes necessary for us to know how arithmetic operations are done in 2's complement. Addition:In 2's complement, we perform addition the same
3 min read
Implementation of XOR Gate from NOR Gate
Implementation of the XOR gate from the NOR gate is possible because the NOR gate is a Universal gate i.e., it can implement all other gates. The NOR gate gives the output 1 if all the inputs are 0. XOR gate is a logic gate that gives output 1 when several 1s are odd. In this article, we will explor
4 min read
Self Starting Counter
A counter is a device which stores the number of times a particular event or process has occurred (according to Wikipedia). As the name suggests, a counter is a device which is used for "counting" - mostly in relation to a clock signal. A counter is said to be self-starting if it is possible to ente
2 min read
Digital Electronics - Radix and Diminished Radix Complements
Prerequisite - Complement of a Number The use of complements is to mainly perform Subtraction. We can easily perform addition in contrast if we would like to implement subtraction using logic gates we require more (because we need to consider borrowing that kind of stuff). So if we somehow make it i
4 min read
Implementation of NOT Gate using NAND Gate
A universal gate is a logic gate that can be used to implement other types of logic gates. In other words, using a universal gate, you can do all the simple operations like AND, OR, NOT, NAND, and NOR. The two most general purpose NAND gates and NOR gates. These gates are considered universal becaus
5 min read