Boolean Algebra
Basic Gates NOT or Inverter
Inversion or complement
X
Y=X
X Y = X
0
1
1
0
Graphical representation
Truth-table
Serves as a definition
of the operation
X is usually pronounced X-dash (or not-X)
2
Basic Gates - AND
AND operation
Y is 1 iff A

Karnaugh Maps
K-map groupings
Entering terms from TT & expressions
Minterm & Maxterm location
K-map simplification
Karnaugh Maps
Karnaugh Maps (K-maps) may be used
to design implementations of logic
functions using:
2-level SOP, or
2-level POS
which are

Multiplexers, Decoders and
Programmable Logic
Multiplexers, Decoders and Simple
PLDs
Multiplexers
Digital equivalent of a multi-way switch
N1 (directional).
SS
O
D0
S1S0 D0
D1
S1S0D1
D2
S1S0D2
D3
S1 S 0 D 3
S0
S1
4 to 1 mux.
1 0
O
D0
D1
D2
D3
00
D0
01
D1

School Of Engineering
Electronic and Electrical Engineering
Multi-Level Gate Circuits
NAND and NOR Gates
Outline
1. Multi-Level Gate Circuits
2.
3.
4.
5.
6.
7.
NAND and NOR Gates
Design of Two-Level Circuits Using NAND and NOR Gates
Design of Multi-Level

Sequential Circuits
State Machines
State Machines
Basic Idea:
We want a box that can behave differently
according to what has happened previously it
remembers history.
It responds to current inputs to produce current
outputs which are also based upon its

Hazards
Propagation Delays
Hazards
Gate Delays
Physical implementations of gates will
have finite delays between input
changes and corresponding output
changes.
The input change is said to propagate
through the circuit
These delays are referred to as
Prop

Application of Boolean Algebra
Formulating Equations
Example
Mary watches TV if it is Monday night and she
has finished her homework.
Let F = 1 iff Mary watches TV
Let A = 1 iff it is Monday night
Let B = 1 iff she has finished her homework
Then F = A . B

Latches and Flip-flops
Latch and flip-flop
2
Minimal 2-state System
Q
Circuit has two stable
states.
Problem how to force
state change?
0
1
Q
1
0
Q
3
Set-Reset Latch
Q
S
R
Set (S) may be used to force a 1 on Q (S=1, R=0)
Reset (R) may be used to force a 0

EEE 244
Introduction to Logic Design
Text Book
Available in NU library
Topics covered include:
Introduction to class and to digital logic;
Boolean Algebra
Boolean Algebra: Theorems and Applications
Logic minimization
Combinational Logic
Large Logic

Registers and Counters
Registers
A collection of flip-flops with a common clock
that is treated as a unit. Typically used to
store or manipulate a multi-bit value.
Q3
Q2
Q1
Q0
Q
4
Clr
Q
Clr
Q
Clr
Q
Clr
Q
Clr
Q
CE
D
CE
D
CE
D
CE
D
CE
D
Clock
ClrN
Load
Cloc