University of Waterloo
Department of Electrical and Computer Engineering
ECE223
Digital Circuits and Systems
Final Examination
15 April, 2008
12:30 3:00PM
Instructors: O. Basir (Section 1) and F. Karray (Section 2)
Name: _
Student ID: _
Instructions:
No a
Department of Electrical and Computer Engineering
ECE 124: Digital Circuits and Systems
Winter Term 2015
COURSE INSTRUCTORS:
Name
Andrew Kennings
Class
LEC001/LEC002
Office
EIT 4102
Ext
36909
Email
[email protected]
LAB INSTRUCTORS:
Name
Bahaedinn
Deriving logic functions from truth tables
I Given a truth table, we might want to derive a logic function (the function is
easier to manipulate).
I Two simple ways to derive a logic function one method will yield a
SumOfProducts (SOP) representation fo
Karnaugh maps (KMaps)
I Karnaugh maps are an alternative way (compared to a truth table) to describe
logic functions; they are useful for displaying logic functions with up to 4 or 5
inputs.
I Whereas truth tables describe a function in a tabular format,
Signed number representations
I
I
We might also want to represent signed integers in different
bases.
One simple way to do this would be to use a sign bit; Given
the representation of a number in n digits, we could add
another digit:
I
I
I
Example. Repres
Binary variables and functions
I
A binary variables is a variables that take on only two discrete
values 0 and 1.
I
A binary logic function produces an output as an expression of
its inputs. Its inputs are binary variables and/or other binary
logic functi
Unsigned number representations
I
Digital circuits and systems are a means to perform
computation and logical operations via machines.
I
Weve considered logic equations, but we also need to
understand how to represent values (numbers). Need to
consider ho
Interesting things about XOR
I Recall that I mentioned XOR gates are useful in arithmetic circuits (e.g., to
build adders) and other sorts of circuits.
I Sometimes, we can discover a XOR gate buried or hidden inside of a
logic expression. If we can find i
Circuits implemented with only NAND and/or NOR
I We can implement any circuit with AND, OR, and NOT gates, but we can
implement any circuit using only NAND or NOR (or a combination of the two
types).
I We might do this for certain considerations e.g., due
Other types of logic gates
I Although AND, OR, and NOT gates are sufficient to implement any circuit,
there are other useful types of logic gates.
I Useful typically means that we can implement things more efficiently
using these types of gates.
January 4
Boolean algebra
I
Introduced in 1854 by George Boole. Shown in 1938 to be
useful for manipulating Boolean logic functions by C. E.
Shannon.
I
Postulates and theorems for Boolean algebra are useful to
simply logic equations, demonstrate equivalence of
expr
Fixed point representations
I
If we have values with fractional parts, one way to represent
them is to consider using a fixed point representation.
I
In this representation, we allow a certain number of digits
prior to the fixed point (the unsigned intege
ECE 124 Review
Chapter 2
Logic Gates, their symbols and Truth Tables
AND Gate
OR Gate
NOT Gate
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Student ID Number:_
University of Waterloo
Final Examination
Term: WINTER
Year:2010
Student Name
UW Student ID Number
Course Abbreviation and Number
ECE223
Course Title
Digital Circuits & Systems
Section(s)
001,002
Sections Combined Course(s)

Section Nu
Department of Electrical and Computer Engineering
ECE 124: Digital Circuits and Systems
Winter Term 2014
COURSE INSTRUCTORS:
Name
Andrew Kennings
Class
LEC001/LEC002
Office
EIT 4102
Ext
36909
Email
[email protected]
LAB INSTRUCTORS:
Name
Mohamed H. Ah