## Analysing Logic Circuits

A typical logic circuit problem will give you a logic circuit to analyse.  A common question might be something like this one:

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In this case, you’ve got to work out what the final output of the logic circuit at the far right is.  What you need to do is work your way bit by bit through each part of the circuit.

So if we start with the top NOT gate – it has just one input – x.  So the output is going to be ‘NOT x’, or  in logic notation.  Moving down to the middle connector on the left – the OR gate – it has 3 inputs, x, y and z.  So the output of this gate is going to be .  The bottom left gate is an AND gate – but be careful.  The inputs are not x, y, and z. They’re actually, x, x and z – the x is input twice.  So the output is going to be .  After having done this much, we can put this information into our diagram:

We can move to the next stage of the logic circuit now.  There are two more gates – an AND gate with three inputs, and an OR gate with two inputs.  However, if you look at how everything is connected, you can work out that you can’t do the OR gate until you’ve done the AND gate.  This is because the output of the AND gate leads directly into the OR gate.  So let’s do the AND gate first.  It has three inputs – ,  and .  So the output is going to be:

Notice how I’ve used brackets to keep each of the inputs separate in the expression for the output.  Because the inputs themselves are logic expressions (for instance the  input), they need to be evaluated first.  That’s why we use the brackets.

This output from the AND gate is one of the inputs into the final OR gate.  The other input comes from the output of the bottom left AND gate – .  So after feeding these two inputs into the final OR gate, we should get: