Logic Circuits in Computer Architecture
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Programming for GCSE
Topic 9.1: Logic Circuits
T
eaching
L
ondon
C
omputing
William Marsh
School of Electronic Engineering and Computer Science
Queen Mary University of London
Aims
•
Show how computers are built from logic
gates
•
Logic gates
•
… and truth tables
•
… and boolean algebra
•
…
•
Circuit for Adding
Teaching Issue
•
How to provide a coherent, joined up view
•
Some curricula include logic circuits but it is not
related to operation of a computer
•
Logic circuits
add binary numbers
computer
architecture
L
OGIC
G
ATES
And, Or, Not
Logic Gates
•
Logic gates are electronic components
•
Transistors
•
Gates behave like switches
•
Two states
•
State represented by a boolean variable
open, X = 0
closed, X = 1
Basic Logic Gates
•
OR gate
•
AND gate
X
Y
X
X
Y
X
Y
Y
NOT Gate
•
Only 1 input
X
not X
X
not X
Basic Logic Gates
OR gate NOT gate
AND gate
X
Y
X
Y
X
not X
Connecting Gates
•
Output of one gate connects to input for next
X
0
X
1
Y
X
2
T
RUTH
T
ABLES
F
OR
C
IRCUITS
AND, OR
•
OR gate
•
AND gate
X
Y
X
Y
X Y X . Y
0 0 0
0 1 0
1 0 0
1 1 1
X Y X + Y
0 0 0
0 1 1
1 0 1
1 1 1
Circuit to Truth Table
•
Test a circuit
X
0
X
1
Y
X
2
X2 X1 X0 Y
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Circuit to Truth Table
•
Test a circuit
X
0
X
1
Y
X
2
X2 X1 X0 Y
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0
1 0 1
1 1 0
1 1 1
Circuit to Truth Table
•
Test a circuit
X
0
X
1
Y
X
2
X2 X1 X0 Y
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
Two circuits
equivalent if (and
only if) they have
the same truth
table
T
RANSLATING
C
IRCUITS
TO
B
OOLEAN
A
LGEBRA
Circuit to Formula
•
Label each point in
turn
X
0
X
1
X
2
X
0
or X
1
(X
0
or X
1
)
and X
2
not X
1
((X
0
or X
1
)
and X
2
) or not X
1
De-Morgan
’
s Laws – Recap
•
Important law for exchanging AND with OR
( A . B ) = A + B
‘
A and B
’
is false when
either A is false or B is
false
( A + B ) = A . B
‘
A or B
’
is false when
both A is false and B is
false
De-Morgan
’
s Law II
•
Same with circuits
•
Quiz
: draw the other law as a circuit
A
B
A
B
De-Morgan
’
s Law III
•
Second law as a circuits
Summary
•
Logic circuits
•
Build a computer
•
Truth table
•
Specify a circuit
•
Boolean expression (formula)
•
Algebraic rules
•
All express same thing
•
Translate from one to other
Explore the world of logic circuits through this comprehensive guide. Learn about logic gates, truth tables, and how computers are built from these components. Discover the basics of logic gates like AND, OR, and NOT, and delve into connecting gates to create functional circuits. Enhance your understanding by observing circuit-to-truth table mappings and grasp how these circuits process information.
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Presentation Transcript
TeachingLondon Computing Programming for GCSE Topic 9.1: Logic Circuits William Marsh School of Electronic Engineering and Computer Science Queen Mary University of London
Aims Show how computers are built from logic gates Logic gates and truth tables and boolean algebra Circuit for Adding
Teaching Issue How to provide a coherent, joined up view Some curricula include logic circuits but it is not related to operation of a computer Logic circuits add binary numbers computer architecture
LOGIC GATES And, Or, Not
Logic Gates Logic gates are electronic components Transistors Gates behave like switches Two states State represented by a boolean variable closed, X = 1 open, X = 0
Basic Logic Gates X OR gate X Y Y AND gate X Y X Y
NOT Gate X not X not X Only 1 input X
Basic Logic Gates OR gate NOT gate X X not X Y AND gate X Y
Connecting Gates Output of one gate connects to input for next X0 X1 Y X2
AND, OR True when either X or Y true OR gate X Y X + Y 0 0 0 0 1 1 1 0 1 1 1 1 X Y True when both X and Y true AND gate X Y X . Y 0 0 0 0 1 0 1 0 0 1 1 1 X Y
Circuit to Truth Table X0 X1 Test a circuit Y X2 X2 X1 X0 Y 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
Circuit to Truth Table X0 X1 Test a circuit Y X2 X2 X1 X0 Y 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1
Circuit to Truth Table X0 X1 Test a circuit Y X2 X2 X1 X0 Y 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Two circuits equivalent if (and only if) they have the same truth table
TRANSLATING CIRCUITSTO BOOLEAN ALGEBRA
Circuit to Formula ((X0 or X1)and X2) or not X1 Label each point in turn X0 or X1 (X0 or X1)and X2 X0 X1 X2 not X1
De-Morgan s Laws Recap Important law for exchanging AND with OR A and B is false when either A is false or B is false ( A . B ) = A + B A or B is false when both A is false and B is false ( A + B ) = A . B
De-Morgan s Law II ( A + B ) = A . B Same with circuits A A B B Quiz: draw the other law as a circuit
De-Morgan s Law III ( A . B ) = A + B Second law as a circuits A A B B
Summary Logic circuits Build a computer Truth table Specify a circuit Boolean expression (formula) Algebraic rules All express same thing Translate from one to other
