### The Surprising Similarity Between A Full Subtractor And Its Output

Dated : 03-Feb-2023

Category : Education

# The Surprising Similarity Between a Full Subtractor and Its Output

When it comes to digital circuits, the output of a full subtractor is surprisingly similar to the full subtractor itself. This fascinating concept is integral to understanding digital circuits and how they process information. In this blog post, we'll explore what a full subtractor is, how it works, and how the output of a full subtractor is the same as the full subtractor.

## What is a Full Subtractor?

A full subtractor is a digital circuit that takes two binary digits (also known as bits) as inputs and outputs the difference between them. This circuit is also known as a binary subtractor, a half-subtractor, or a three-bit subtractor. The full subtractor's main purpose is to subtract one binary number from another. It can also be used to perform subtraction with borrow, which is a type of arithmetic operation that requires borrowing a bit from the next column to the left.

A full subtractor consists of three inputs (A, B, and C) and two outputs (D and B). A is the minuend, B is the subtrahend, and C is the borrow bit. The two outputs of the full subtractor are D (difference) and B (borrow). The difference output D is the result of subtracting the subtrahend B from the minuend A. The borrow output B is used to indicate if a borrow is needed from the next column to the left.

## How Does a Full Subtractor Work?

A full subtractor operates by taking two binary numbers (A and B) and subtracting them. The borrow bit C is used to indicate if a borrow is needed from the next column to the left. The subtractor then produces two outputs, the difference output D and the borrow output B.

The difference output D is calculated using the following equation: D = A - B - C. This equation states that the difference output D is equal to the minuend A minus the subtrahend B minus the borrow bit C.

The borrow output B is calculated using the following equation: B = A - (B + C). This equation states that the borrow output B is equal to the minuend A minus the sum of the subtrahend B and borrow bit C.

## How is the Output of a Full Subtractor the Same as the Full Subtractor?

The output of a full subtractor is surprisingly similar to the full subtractor itself. This is because the output of a full subtractor is simply the difference between the minuend A and the subtrahend B minus the borrow bit C. This difference is the same as the equation used to calculate the difference output D, which is A - B - C. Therefore, the output of a full subtractor is the same as the full subtractor itself.

## Conclusion

The output of a full subtractor is surprisingly similar to the full subtractor itself. A full subtractor is a digital circuit that takes two binary digits

Computer Science
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