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Implement following questions using NAND gate only:

i) F = ∑m (1,2,3,4,7,11,13) + d(9,15)
ii) F = ∏M (4,5,6,7,8,12) + d(1,2,3)

Mumbai University > ELECTRO > Sem 3 > Digital Circuits and Designs

Marks: 10M

Year: Dec 2013

1 Answer
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A Karnaugh map provides a pictorial method of grouping together expressions to minimize a given boolean function.

(i) Consider the following function.

F = ∑m (1,2,3,4,7,11,13) + d(9,15) It is given in terms of minterms, hence the minimized expression will be in the form of SOP. The K-map minimization of the given function is as follows:

enter image description here

Implementation of the above minimized expression using NAND gates is shown below:

enter image description here

(ii) Consider second function.

F = ∏M (4,5,6,7,8,12) + d(1,2,3) It is given in terms of maxterms, hence the minimized expression will be in the form of POS. The K-map minimization of the given function is as follows:

enter image description here

Since the implementation is to be done using NAND gates, we will convert the POS into SOP. After conversion, the function is implemented as follows:

enter image description here

2

i think your second question (F = ∏M (4,5,6,7,8,12) + d(1,2,3)) figure is wrong...... the sign u've given of and gate ,,,,,,,while it should be or gate sign.


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