Electrical – Symbolic logic operator “implication” to logical gates

logic-gates

I need to translate a symbolic operator to a logical gates circuit.

Following the table that the symbolic operator has:

P Q Result
1 1 1
1 0 0
0 1 1
0 0 1

Any idea how can I make it?

This is a draft of solution

enter image description here

Best Answer

A simple solution for such puzzles is counting the one and zeroes at the output:

  • all zero or all one → trivial
  • one zero and three ones → OR gate (or NAND gate)
  • one one and three zeroes → AND gate (or NOR gate)
  • two zeroes and two ones → trival (copy P or Q) or XOR or XNOR gate
P Q   R
1 1   1
1 0   0
0 1   1
0 0   1

Three ones. So we have an OR gate at the output. Let's take a look at the case where R is zero: An OR gate needs two zeroes to create a zero. So we have to invert P before feeding it into the gate.

P  -P Q   R
1   0 1   1
1   0 0   0
0   1 1   1
0   1 0   1

Let's order the lines the "normal" way:

P  -P Q   R
1   0 0   0
1   0 1   1
0   1 0   1
0   1 1   1

I think you can see now the solution is inverting the P input, then feeding -P and Q into an OR gate.

Related Topic