Truth Tables, Boolean Expressions, and Boolean Algebra (Lecture #3). ECE 331 – Digital System Design. The slides included herein were taken from the materials accompanying Fundamentals of Logic Design, 6 th Edition , by Roth and Kinney,
4 variables → 24 = 16 rows
(and Logic Circuits)
Literals highlighted in green
Logical operators highlighted in blue
Using a truth table, evaluate the following Boolean expressions:
F1(A,B,C) = A'.B.C'
F2(A,B,C) = A + B' + C'Boolean Expressions: Example #1
Simple AND and OR Functions
An AND function = 1
when all literals = 1.
An OR function = 1
when any literal = 1.
Literal = X or X'
If X' = 1 then X = 0
If X' = 0 then X = 1
An OR function = 0
when all literals = 0.
6. X + Y = Y + X 6D. XY = YX
7. (X + Y) + Z = X + (Y + Z) 7D. (XY)Z = X(YZ) = XYZ
= X + Y + Z
8. X(Y+Z) = XY + XZ 8D. X + YZ = (X + Y)(X + Z)
9. XY + XY' = X 9D. (X + Y)(X + Y') = X
10. X + XY = X 10D. X(X + Y) = X
11. (X + Y')Y = XY 11D. XY' + Y = X + Y
12. (X + Y + Z +...)' = X'Y'Z'... 12D. (XYZ...)' = X' + Y' + Z' +...
13. (X + Y + Z +...)D= XYZ... 13D. (XYZ...)D = X + Y + Z +...
Theorem for multiplying out and factoring:
14. (X + Y)(X' + Z) = XZ + X'Y 14D. XY + X'Z = (X + Z)(X' + Y)
15. XY + YZ + X'Z = XY + X'Z
15D. (X + Y)(Y + Z)(X' + Z) = (X + Y)(X' + Z)