Digital Systems and Microprocessors
• Dr. Reza Sedaghat
• COE 328: Digital Systems and Microprocessors
• Office: Room ENG431
• Office hours: Check Department front office
• Email address: rsedagha@ee.ryerson.ca
• Course References:
• Brown, S. Fundamentals of Digital Logic with VHDL Design,
Mc Graw Hill, 2009 (Course Text)
• Wakerly J. F. Digital Design Principles and Practices, Prentice Hall, 1994
• Hayes. J. P. Introduction to Digital Logic Design, Addison Wesley, 1993
• Dewey, A. Analysis and Design of Digital Systems with VHDL, TPC, 1997
TM
UNIVERSITY
L(x) = x
Since L = 1 if x = 1 and L = 0 if x = 0, we can say that
1
Logical AND
L(x , x ) = x ꞏ x
1
2
1
where L = 1 if x1 = 1 and x2 = 1,
L = 0 otherwise.
Logical OR
2
L(x , x ) = x + x
1
2
1
2
where L = 1 if x1 = 1 or x2 = 1 or if x1 = x2 = 1,
L = 0 if x1 = x2 = 0.
The
2
L(x , x , x ) = (x1 +
1
2
3
x) ꞏ x
2
3
3
Logical NOT
L(x) = x
where L = 1 if x = 0,
L = 0 if x = 1
4
5
6
7
Timing Diagram
Timing Diagram has same values as truth table + TIMING, t0, t1,…, tn
t0
t1
t2
X1=0
X1=0
X1=1
X1=1
X2=0
X2=1
X2=0
X2=1
f=1
f=1
f=0
f=1
8
Functionally Equivalent Networks: Different Circuit but
same Truth Table
Exercise: Find the Truth table from above circuit?
Answer: Same as truth table from previous slide (#8)
Different Circuit but same Truth Table
9
Axioms of Boolean Algebra
Single-Variable Theorems
10
11
Two- and Three-Variable Properties
Formal Proof LHS = RHS
For example: Proof of DeMorgan’s theorem in 15a
Same LHS and RHS
12
Examples:
Do the examples 2.1 and 2.2 end of section 2.5
13