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. Karr
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
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 input
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 di
Karnaugh maps (K-Maps)
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 Wherea
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 meth
ECE 124 digital circuits and systems
Assignment #5
Q1: In class we designed a comparator for two, n-bit unsigned binary numbers A and B by deriving 2 level
SOP for (A = B), (A > B) and (A < B). Such c
ECE 124 digital circuits and systems
Assignment #7
Q1: A bi-directional shift register can shift both left-to-right and right-to-left. Design a bi-directional shift
register than also has a parallel-l
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
ak
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 o
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).
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
Sect
Q3:
S1 0 0 1 1
S2 0 1 0 1
Behavior Hold Current Value Shift left Shift Right Parallel Load
A 4-bits Universal Shift register is shown as below:
Parallel Outputs
Parallel Inputs
Q4-a (i) Case 1: Sequen
ECE 124 Review
Chapter 2
Logic Gates, their symbols and Truth Tables
AND Gate
OR Gate
NOT Gate
x
y
f
x
y
f
x
f
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
x
y
f
0
0
1
0
1
0
x
y
f
1
0
0
x
y
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
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
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
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
ak