A logic circuit has two inputs A and B. Gate 1 is a NAND gate with inputs A and B…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A logic circuit has two inputs and . Gate 1 is a NAND gate with inputs and . Gate 2 is a NOR gate with inputs and . Gate 3 is an XOR gate whose inputs are the outputs of gates 1 and 2. Gate 4 is a NOT gate that takes the output of gate 3, and its output is . A signal source applies the four input patterns in turn, in the order , , and . Find the output for each pattern. Then say which single gate the whole circuit behaves like. Work out the outputs of gates 1 to 3 on the way, so that you can check each row.
Need a reminder? The key ideaShow
A truth table has rows for inputs. NOT: . OR: . AND: . NAND: . NOR: . XOR: , which is when the inputs differ. De Morgan: and .
The worked solution
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.
Given. Gate 1 is NAND, gate 2 is NOR, gate 3 is XOR of gates 1 and 2, and gate 4 is NOT.
Plan. Write the value on every wire, one row for each input pattern.
- Row : gate 1 gives , gate 2 gives , gate 3 gives , and .
- Row : gate 1 gives , gate 2 gives , gate 3 gives , and .
- Row : gate 1 gives , gate 2 gives , gate 3 gives , and .
- Row : gate 1 gives , gate 2 gives , gate 3 gives , and .
Step 1. Row . NAND gives and NOR gives . XOR of two equal inputs is . NOT gives .
Step 2. Rows and . NAND gives and NOR gives . XOR of different inputs is . NOT gives .
Step 3. Row . NAND gives and NOR gives . XOR gives . NOT gives .
Answer: . This is the output of an XNOR gate: it is when the inputs are equal. Gate 3 alone is an XOR gate for and .
Check. The outputs of gates 1 and 2 are never both together except in row , and then XOR gives . It fits.
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