Thread: how to convert truth table into boolean expressions?

I was wondering if someone can show me a clean cut method to finding boolean expressions for any truth table..

I'll show you an example...

x y z | f(x,y,z)
1 1 1 0
1 1 0 1
1 0 1 1
1 0 0 1

how would we go on about finding an expression for this ??

Hello Khonics89

Originally Posted by Khonics89

I was wondering if someone can show me a clean cut method to finding boolean expressions for any truth table..

I'll show you an example...

x y z | f(x,y,z)
1 1 1 0
1 1 0 1
1 0 1 1
1 0 0 1

how would we go on about finding an expression for this ??

I hope you realise that this is not a complete truth table for three input variables, and . You have only the four lines where ; you need another four lines with to complete the table.

Nevertheless, to answer your question:

• Look for the lines of the table where the output value is 1 (True)

• For each of these lines, construct a logical expression, using AND and NOT as appropriate, to construct the expression that corresponds to the True-False values of the input variables. (See below for examples.)

• Combine each of these expressions using OR's to give a single Boolean expression to represent the output of the complete table.

• If desired (and if you can!), simplify the resulting Boolean expression.

In the (part-)example that you quote, on lines 2, 3 and 4.

On line 2, and are True; is False. So this line is AND AND (NOT ); or

On line 3, is True; is False; is True. So this line is

Similarly line 4 is

Combining these three expressions using OR's then, we get:



(This could then be simplified to , if your Boolean algebra is up to it.)

Grandad

thanks grandad- so our main aim is to write individual expressions for each row and then sum them up using "or"

and then simplify if possible ??

Originally Posted by Khonics89

thanks grandad- so our main aim is to write individual expressions for each row and then sum them up using "or"

and then simplify if possible ??

That's a brief summary of what I said, yes.

Grandad