Question

In this problem we’ll explore the fact that all logical circuits can be implemented using just NAND gates.

i. Let’s denote p NAND q as p ? q. Write a logical expression for the three circuits corresponding to AND, OR, and NOT.

ii. ( Validate your three logical expressions with three truth tables. For clarity and full credit, show each variable and distinct statement in a separate column, culminating in your final formula. For instance, if we wanted a table for the statement (p ∧ q) ∨ q, we would need one column for p, one for q, one for p ∧ q and one for the whole statement.

Answer 1

Please go through the solution given below.If find any difficulty,feel free to ask in comment section.Please do upvote this answer.Thank you.

Using NAND and NOR gate all other basic logic gates can be implemented.So these gates are called Universal gates

NAND = short of Not AND. As the name implies NAND gate form by inverting AND gate's output.So if AND gate produce 0 it's corresponding NAND gate gives 1.Similarly if AND gate produce result 1 it's corresponding NAND gate gives result 0.

AND gate by using NAND gate

p_^q = (p NAND q)NAND (p NAND q)

p	q	p^q	p NAND q	(p NAND q)NAND (p NAND q)
0	0	0	1	0
0	1	0	1	0
1	0	0	1	0
1	1	1	0	1

OR gate by using NAND gate

pVq = (p NAND p)NAND (q NAND q)

p	q	pVq	p NAND p	q NAND q	(p NAND p)NAND (q NAND q)
0	0	0	1	1	0
0	1	1	1	0	1
1	0	1	0	1	1
1	1	1	0	0	1

NOT gate using NAND gate

~p =p NAND p

p	~p	p NAND p
0	1	1
1	0	0

Note: since the symbol for NAND in the question is not seen. This answer use the name NAND itself. Please form the answer according to the symbol given in the question.