Boolean Algebra

Emerson

I think this is probably the best forum for this, since there's no real electronics forum.

I've got an exam in this stuff @ 9.30 tomorrow so I'm pretty desperate at this stage...

Wondering how do you draw a truth table for a ciruit whose boolean equation is:
x = (a+ b)(a[+]c)
^
|
xor

Think it goes something like, not sure what goes under the X(of course):

A B C X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

cerebus

The truth table for that function looks like this (I hope - also, I'm guessing you mean [+] represents the xor)

A B C X
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0

Learning this example off is not going to be much good for exam purposes if you don't understand how to derive a truth table...

Try to decompose the function into simple parts - in this case the function evaluates to true iff

(a OR b) AND (a XOR C)

is true.

Think of (a OR b) and (a XOR C) as two new terms - lets call them i = (a OR b) and j = (a XOR c). Try writing a new truth table with those two intermediate steps in there, and then use (i AND j) to get your result x.

A B C I J X
0 0 0 0 0 0
0 0 1 0 1 0
0 1 0 1 0 0
0 1 1 1 1 1
1 0 0 1 1 1
1 0 1 1 0 0
1 1 0 1 1 1
1 1 1 1 0 0

I do hope that helps - good luck tomorrow.

Emerson

Hey,
That's great.. I understood truth tables ok, but was confused how XOR is used and also with one input being used twice.
I actually now understand it. Tried another example and got it out alright using D & E (you used I & J as eg).

thanks for the help, really do appreciate it!

Boston

What does the XOR term mean, I haven't seen it used in the past? Does it stand for the exclusive OR.

Pacifico

Originally posted by Boston
What does the XOR term mean, I haven't seen it used in the past? Does it stand for the exclusive OR.

Yep its exclusive OR