written 21 months ago by
binitamayekar
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modified 21 months ago

Full Subtractor
 Full Subtractor is a combinational logic circuit that is used to subtract two singlebit 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 1to8 demultiplexer.
Implementation of Full Subtractor Using 1to8 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 B_{out} (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 1to8 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: