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Implementation of Full Subtractor using 1-to-8 Demultiplexer

Question design the circuit and implemention of full subtractor using 1x8 demultiplexer

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## Full Subtractor

• Full Subtractor is a combinational logic circuit that is used to subtract two single-bit numbers.
• It considers borrow of the lower significant stage.
• Thus, a full subtractor can perform the subtraction of three bits.
• Full subtractor contains 3 inputs and 2 outputs (Difference and Borrow) as shown in the below figure:

• Here, we implement a full subtractor using a 1-to-8 demultiplexer.

## Implementation of Full Subtractor Using 1-to-8 DEMUX

• Similar to the multiplexers, demultiplexers are also used for Boolean function implementation as well as combinational circuit design.
• We can design a demultiplexer to produce any truth table output by properly controlling the select lines.
• Consider the case for implementing a demultiplexer circuit to produce the full subtractor output.
• The Truth Table below shows the output of a full subtractor:

• From the above truth table, the full subtractor output D(Difference) can be written as follows:

$$D = f (A, B, B_{in}) = ∑m (1, 2, 4, 7)$$

$$D = A' B' B_{in} + A 'B B_{in}' + A B' B_{in}' + A B B_{in}$$

• The Bout (Borrow) output can be expressed as follows:

$$B_{out} = f (A, B, B_{in}) = ∑m (1, 2, 3, 7)$$

$$B_{out} = A' B' B_{in} + A' B B_{in}' + A B' B_{in} + A B B_{in}$$

• From these Boolean expressions, a demultiplexer for producing full subtractor output can be built by properly configuring the 1-to-8 DEMUX, such that with input D = 1, it gives the minterms at the output.
• Using two OR gates with these minterms, the outputs of difference and borrow can be obtained as shown in the below figure: