Design a Full-adder Using Two 4x1 Multiplexers

Half Subtractor-

Before you go through this article, make sure that you have gone through the previous article on Half Subtractor.

We have discussed-

• Half Subtractor is used for the purpose of subtracting two single bit numbers.
• Half subtractors have no scope of taking into account "Borrow-in" from the previous circuit.
• To overcome this drawback, full subtractor comes into play.

In this article, we will discuss about Full Subtractor.

Full Subtractor-

• Full Subtractor is a combinational logic circuit.
• It is used for the purpose of subtracting two single bit numbers.
• It also takes into consideration borrow of the lower significant stage.
• Thus, full subtractor has the ability to perform the subtraction of three bits.
• Full subtractor contains 3 inputs and 2 outputs (Difference and Borrow) as shown-

Designing a Full Subtractor-

Full subtractor is designed in the following steps-

Step-01:

Identify the input and output variables-

• Input variables = A, B, B_in (either 0 or 1)
• Output variables = D, B_out where D = Difference and B_out = Borrow

Step-02:

Draw the truth table-

Inputs			Outputs
A	B	Bin	Bout (Borrow)	D (Difference)
0	0	0	0	0
0	0	1	1	1
0	1	0	1	1
0	1	1	1	0
1	0	0	0	1
1	0	1	0	0
1	1	0	0	0
1	1	1	1	1

Truth Table

Step-03:

Draw K-maps using the above truth table and determine the simplified Boolean expressions-

Also Read- Full Adder

Step-04:

Draw the logic diagram.

The implementation of full adder using 1 XOR gate, 3 AND gates, 1 NOT gate and 1 OR gate is as shown below-

To gain better understanding about Full Subtractor,

Watch this Video Lecture

Next Article- Ripple Carry Adder

Get more notes and other study material of Digital Design.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Half Subtractor-

• Half Subtractor is a combinational logic circuit.
• It is used for the purpose of subtracting two single bit numbers.
• It contains 2 inputs and 2 outputs (difference and borrow).

Half Subtractor Designing-

Half subtractor is designed in the following steps-

Step-01:

Identify the input and output variables-

• Input variables = A, B (either 0 or 1)
• Output variables = D, b where D = Difference and b = borrow

Step-02:

Draw the truth table-

Inputs		Outputs
A	B	D (Difference)	b (Borrow)
0	0	0	0
0	1	1	1
1	0	1	0
1	1	0	0

Truth Table

Step-03:

Draw K-maps using the above truth table and determine the simplified Boolean expressions-

Also Read- Half Adder

Step-04:

Draw the logic diagram.

The implementation of half subtractor using 1 XOR gate, 1 NOT gate and 1 AND gate is as shown below-

Limitation of Half Subtractor-

• Half subtractors do not take into account "Borrow-in" from the previous circuit.
• This is a major drawback of half subtractors.
• This is because real time scenarios involve subtracting the multiple number of bits which can not be accomplished using half subtractors.

To overcome this drawback, Full Subtractor comes into play.

To gain better understanding about Half Subtractor,

Watch this Video Lecture

Next Article- Full Subtractor

Get more notes and other study material of Digital Design.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Design a Full-adder Using Two 4x1 Multiplexers

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