Question

We know that the NAND gate is universal, so all other gates can be built using just NAND gates. Hence we should be able to build a half-adder using NAND gates. And we can.

a) Draw the AND operation as a circuit using only 2 NAND gates [2 marks]

b) Check your design in (a) by showing the full truth table for it [2 marks]

c) Draw the OR operation as a circuit using only 3 NAND gates [2 marks]

d) Check your design in (c) by showing the full truth table for it [2 marks]

e) Using your answers from above, and by observing that x⊕y = (x+y).(x.y), draw the XOR operation as a circuit using at most 6 NAND gates [2 marks]

f) Check your design in (e) by showing the full truth table for it [2 marks]

Answer 1

AND Operation as a circuit using 2 NAND gates: - cirunit diagram Y Dar ab b for and nand ab.ab gate, output = ao Y cabo Truth table b output of ist NAND = ylcão) 1 OO 1 output of 2nd NAHD = Y Cab) 00o~ Hence, above touth table is the and operation, OR operation using 3 NAND gales: circuit diagram x= • Z= a - 5 b - atb. Y =5

@ Truth table for above circuit У output z(x4) - - 2 which is The output of above circuit is the output of or gate Xor Operation as a circuit using max. 6 NANDI- circuit diagram Q Z 0 Truth table for above circuits a b 21 output a output of xor 1 — - - Hence, for above circuit, output Q is same as the output of xor gate

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