Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A NAND gate is a universal gate. Use the standard constructions to find how many NAND gates are needed to make a NOT gate, an AND gate, an OR gate, a NOR gate and an XOR gate. For XOR, use the standard circuit. Gate 1 takes and . Gate 2 takes and the output of gate 1. Gate 3 takes and the output of gate 1. Gate 4 takes the outputs of gates 2 and 3. A NOT gate is a NAND gate with its inputs tied together.
A truth table has rows for inputs. NOT: . OR: . AND: . NAND: . NOR: . XOR: , which is when the inputs differ. De Morgan: and .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. NOT. One NAND gate with its inputs tied. .
Step 2. AND. One NAND gate, then one more as a NOT. That is gates.
Step 3. OR. A NOT on and a NOT on (two gates), then a NAND gate on the two results: . That is gates.
Step 4. NOR. The OR circuit of gates, then one more as a NOT. That is gates.
Step 5. XOR. The four gates of the standard circuit. Gate 1 gives . Gate 2 gives , gate 3 gives , and gate 4 combines them into .
Answer: for NOT, for AND, for OR, for NOR and for XOR.
Check. Trying all four rows of and for the XOR circuit gives . The program of this lesson does this test.
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