What is a 2 ‘s Complement?
The 2’s complement is a method we use to represent negative numbers in binary arithmetic. To get the 2’s complement of a binary number, you first find its 1’s complement by flipping all the 0s to 1s and all the 1s to 0s. Once you have the 1’s complement, you just add 1 to it, and that gives you the 2’s complement.
Let’s take an example to understand this process. Suppose we want to find the 2’s complement of the binary number 10010. First, we find the 1’s complement, which will be 01101 (changing 0s to 1s and 1s to 0s). Then, we add 1 to it, and the result will be 01110, which is the 2’s complement.
Binary Subtraction Using 2’s Complement: To subtract a smaller binary number from a larger one using 2’s complement subtraction, follow these steps:
Step 1: Determine the 2’s complement of the smaller number.
Step 2: Add the 2’s complement to the larger number.
Step 3: Omit the carry. Note that there is always a carry in this case.
Let’s illustrate these steps with an example:
Binary Subtraction Using 2’s Complement
Binary subtraction using 2’s complement becomes easier when you and I follow a clear set of steps to subtract a smaller number from a larger one.
Step 1: First, we find the 2’s complement of the smaller number.
Step 2: Then, we add it to the larger number.
Step 3: Finally, we ignore the carry. You’ll notice that a carry is always present in this type of subtraction.
Advantages of 2 ‘s Complement
The advantages of both the 1’s complement and 2’s complement methods for subtracting binary numbers lie in their application using logic circuits. Although they may seem complicated compared to the direct method of binary subtraction, they offer distinct benefits:
Both methods allow subtraction to be performed using only addition, which simplifies the implementation using logic circuits.
The 1’s complement and 2’s complement of a binary number can be easily obtained using logic circuits, making them practical for hardware implementations.
The 2’s complement method has an advantage over the 1’s complement method in that it does not involve the end-around-carry operation, which can lead to complexity and potential errors in the calculation.