This preview shows pages 1–4. Sign up to view the full content.
Boolean Algebra
A + 0 = A
A + A’ = 1
A . 1 = A
A. A’ = 0
1 + A = 1
A + B = B + A
0. A = 0
A . B = B . A
A + (B + C) = (A + B) + C
A. (B. C) = (A. B). C
A + A = A
A . A
= A
A.
(B + C) = A.B + A.C
Distributive Law
A + B.C = (A+B). (A+C)
A . B = A + B
De Morgan’s theorem
A + B = A . B
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document De Morgan’s theorem
A . B = A + B
A + B = A . B
Thus,
is equivalent to
Verify it using truth tables.
Similarly,
is equivalent to
These can be generalized to more than two
variables: to
A. B. C = A + B + C
A + B + C = A .
B . C
Synthesis of logic circuits
Many problems of logic design can be specified using a
truth table. Give such a table, can you design the logic
circuit?
Design a logic circuit with three inputs A, B, C and one
output F such that F=1 only when a majority of the inputs is
equal to 1.
A
B
C
F
Sum of product form
0
0
0
0
F = A.B.C + A.B.C + A.B.C + A.B.C
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
Draw a logic circuit to generate F
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/18/2011 for the course 22C 060 taught by Professor Ghosh during the Spring '11 term at University of Iowa.
 Spring '11
 Ghosh

Click to edit the document details