HW Help: Boolean Simplification

Thread Starter

rtran2015

Joined Oct 3, 2015
13
=ABCD' + AB' + AC' + AD' + A'B'C'D'
=AD'(BC + 1) + AB' + AC' + A'B'C'D'; T8 <--- ABCD' + AD'
=AB' + AC' + AD'(1) + A'B'C'D'; T2' Null Element
=AB' + AC' + AD' + A'B'C'D'; T1 Identity
-----------------------------------------------------------
=AC' + AD' + B'(A + A'C'D'); T8
=AC' + AD' + B'(A + C'D'); T10
---------------------------------------------------
=AB' + AC' + AD' + B'C'D'; T8 <--- Everything at minterm?
-----------------------------------------------------------
I can un-distribute A, though these terms seem to be the most simplistic

Y = AB' + AC' + AD' + B'C'D'

if AB' is true, does it matter if the rest is true or false because its in an OR gate?

The truth table for this equation:
A B C D= Y
0 0 0 0 = 1
0 0 0 1 = 0
0 0 1 0 = 0
0 0 1 1 = 0
0 1 0 0 = 0
0 1 0 1 = 0
0 1 1 0 = 0
0 1 1 1 = 0
1 0 0 0 = 1
1 0 0 1 = 1
1 0 1 0 = 1
1 0 1 1 = 1
1 1 0 0 = 1
1 1 0 1 = 1
1 1 1 0 = 1
1 1 1 1 = 0

We can remove all the ones that equal zero

A B C D= Y
0 0 0 0 = 1
1 0 0 0 = 1
1 0 0 1 = 1
1 0 1 0 = 1
1 0 1 1 = 1
1 1 0 0 = 1
1 1 0 1 = 1
1 1 1 0 = 1
 

WBahn

Joined Mar 31, 2012
29,976
=ABCD' + AB' + AC' + AD' + A'B'C'D'
=AD'(BC + 1) + AB' + AC' + A'B'C'D'; T8 <--- ABCD' + AD'
=AB' + AC' + AD'(1) + A'B'C'D'; T2' Null Element
=AB' + AC' + AD' + A'B'C'D'; T1 Identity
-----------------------------------------------------------
=AC' + AD' + B'(A + A'C'D'); T8
=AC' + AD' + B'(A + C'D'); T10
---------------------------------------------------
=AB' + AC' + AD' + B'C'D'; T8 <--- Everything at minterm?
-----------------------------------------------------------
No. A minterm is True for exactly one combination of inputs, which means that it is the AND of all four inputs (some of which might be complemented).

What you have is simply a Sum of Products, or SOP, expression. Which is what you are looking for.

I can un-distribute A, though these terms seem to be the most simplistic

Y = AB' + AC' + AD' + B'C'D'

if AB' is true, does it matter if the rest is true or false because its in an OR gate?
No, it doesn't matter. Any time any term is True, the status of all of the other terms is irrelevant.

The truth table for this equation:
A B C D= Y
0 0 0 0 = 1
0 0 0 1 = 0
0 0 1 0 = 0
0 0 1 1 = 0
0 1 0 0 = 0
0 1 0 1 = 0
0 1 1 0 = 0
0 1 1 1 = 0
1 0 0 0 = 1
1 0 0 1 = 1
1 0 1 0 = 1
1 0 1 1 = 1
1 1 0 0 = 1
1 1 0 1 = 1
1 1 1 0 = 1
1 1 1 1 = 0

We can remove all the ones that equal zero

A B C D= Y
0 0 0 0 = 1
1 0 0 0 = 1
1 0 0 1 = 1
1 0 1 0 = 1
1 0 1 1 = 1
1 1 0 0 = 1
1 1 0 1 = 1
1 1 1 0 = 1
And what does this accomplish? If you are going to show a truth table, then show a truth table.
 

Thread Starter

rtran2015

Joined Oct 3, 2015
13
Got it

Thank you very much for your help, patience, and examples

I should be able to get through most of this homework assignment
 
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