Truth Tables and Logic Diagrams
Jackie Dawes
School of Computing
Teesside University
Which bit is this?
This session is designed to support the development of
lesson plans for the Binary Logic, Truth Tables and Logic
Diagrams part of the GCSE curricula:
 Explain why data is represented in computer
systems in binary form
 Understand and produce simple logic diagrams
using the operations NOT, AND and OR
 Produce a truth table from a given logic diagram
Explain why data is represented in
computer systems in binary form
Binary
• Every computer processor is made of millions
of tiny switches that can be turned off or on, i.e.
they only have two states
• Computers need a number system that only has
two digits: the binary number system
• The two binary digits (0 and 1) are called bits and
correspond to the off/on positions of the switches
in the computer processor
Binary and logic
• Logic in computing is very simple, it either is or it isn’t
• There are three common ways to represent logic in computing:
– Logic Circuit diagrams
– Truth Tables
– Boolean expression
• Computer circuits use bits
– 0 means a 0V voltage input
– 1 means a 5V or a 3.3V voltage input
• Logic gates and logic diagrams use bits
– 0 means false
– 1 means true
Understand and produce simple logic diagrams using
the operations AND, NOT, and OR
Logic Gates and Truth Tables
• Logic gates are very basic components in any
computer – e.g. the CPU is constructed from logic
gates
• The gates we are looking at today are AND, OR
and NOT
• They take one or more inputs and produce an
output
• A single gate can be as simple as on/off switch,
on = true, off = false
• Gates can be used together to show the outcome
when a combination of events happen
Logic Gates and Truth Tables
continued…
• A truth table is a table of 1s and 0s arranged
to show the results (outputs) from all possible
inputs. Eg
Inputs
A
Output
B
C
Z
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
GCSE Logic Gates
http://www.docstoc.com/docs/21954668/Elementary-Logic-Gates
Inverter (NOT Gate)
• this gate will invert the input
• It has one input
• This is the symbol used for a NOT gate
• So, Z = A
Truth Table for an Inverter
A
Output
0
1
1
0
AND Gate
• It has at least two inputs
• Its output will only be 1 when all the inputs are 1,
otherwise the output will be 0
• This is the symbol for an AND gate
• So, Z = A.B (a dot is used to show the AND
operation)
Truth table for an AND gate
A
B
Z
0
0
0
0
1
0
1
0
0
1
1
1
OR Gate
• It has at least two inputs
• Its output will be 1 when any of the inputs are 1
• This is the symbol for an OR gate
• So Z = A+B ( a plus is used to show the OR
operation)
Truth Table for an OR Gate
A
B
Z
0
0
0
0
1
1
1
0
1
1
1
1
http://logic.ly/demo/
Playing with Gates
Produce a truth table from a given logic diagram
Logic Diagrams
• Logic diagrams use a symbolic description of
logic gates
• The gates are combined to represent a
particular logic expression, e.g.
Creating truth tables from logic
diagrams
• Process:
– Select each combination of inputs one at a time
– Replace their inputs with their respective values
– Follow the output through the diagram until the
output is reached
– List the final output for each state in the truth table
next to the value of each input
– Easier to do than to say, so……
• Do the Exercise (separate hand-out)
Boolean Values and Operators
• We can produce truth tables from a variety of
sources, e.g. to represent these situations we
could write:
Boolean value
– if the burglar alarm rings then
call the police
Boolean value
– if the alarm clock goes off and
it’s a week day then
get up
Boolean value
else
go back to sleep
Boolean operator
Based on slides produced by Jay Chapman and Tyrone Davison, Teesside University
Truth Tables
programming language syntax
Action
if the burglar alarm rings
then
Boolean value
call the police
Based on slides produced by Jay Chapman and Tyrone Davison, Teesside University
Truth Tables
Boolean value
Boolean value
if the alarm clock rings and it’s a week
day then
Action on True
Boolean operator
get up
else
Action on False
go back to sleep
Based on slides produced by Jay Chapman and Tyrone Davison, Teesside University
Questions?
Jackie Dawes
School of Computing
Teesside University