NAND Gate question?

Truth table:





A B C Y


0 0 0 0


0 0 1 1


0 1 0 0


0 1 1 1


1 0 0 1


1 0 1 0


1 1 0 1


1 1 1 0





A, B, C(input), Y(output)





a) Plot a K-map for the function and derive the min sum-of-product Boolean expression using K-map.





Ans: Y = AC’ +A’C





b) Redesign the circuit using only NAND gate. Show the expression and draw the logic circuit.





I having trouble on part b. Your help is greatly appreciated.





Tks!!!

NAND Gate question?
a) K-MAP in SOP form is correct: AC'+A'C





b) to make the circuit using NAND gates, you will need 5.


A' and C' will require both inputs tied together (2 gates)


then make A'C and AC' (2 more gates) and send the outputs to one last NAND gate.





Just remember how to make NOT AND OR gates from NAND.





There is software to help you draw and create the functions from kmap. I recommend the simple version from karnaugh.shuriksoft.com, it will create the diagrams in POS/SOP using AND/OR and NAND gates.
Reply:Y = (A C')' * (A' C)'





You can get C', A', (AC')' and (A'C)' by connecting that particular line to both inputs of the nand gate.





Ex


(A * A)' = A'