# Advanced Digital Design Discussion – concepts used in the design of adders and subtractors

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Attachments:Demonstrate concepts used in the design of adders and subtractors

A full subtractor handles one bit of the binary subtraction algorithm, having input bits X (minuend), Y (subtrahend), and BIN (borrow in), and output bits D (difference) and BOUT (borrow out). You can write logic equations corresponding to the binary subtraction table as follows:

D = X XOR Y XOR BIN
BOUT = X̄Y + X̄BIN + YBIN

These equations are very similar to equations for a full adder, which should not be surprising. A two’s-complement subtraction operation, X – Y, can be performed by an addition operation, namely, by adding the two’s complement of Y to X. The two’s complement of Y is (Y’ + 1), where Y’ is the bit-by-bit complement of Y.

On the basis of the explanation given above, respond to the following:

• How would you design a full-subtractor using a full-adder?
• What are some of the applications of full-adder other than the full-subtractor? List and describe two of these applications.
• Two responds to the conclusion – in favor or against the outcome / conclusion.

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