GCSE

Computing#BristolMet

Session Objectives

#5

MUST explain why data is represented in computer systems in binary

SHOULD understand and produce simple logic diagrams using the operations NOT,

AND

and

OR

COULD construct a truth tables from a given logic diagram

Create a program using the LMC to calculate the perimeter of any

given quadrilateral. Try to design it so that it gives a running total.

GCSE

Computing#BristolMet

Binary Logic

Starter:

A lily pad doubles in size everyday. It takes 30 whole days to

fill up the whole pond, how many days did it take to fill half

the

pond? Prove your answer...

GCSE

Computing#BristolMet

Binary Logic

We know that from von Neumann and the principle that all modern

computers, data and instructions are based on the binary system

(base 2). This is due to the ease in which 2 states can

recognised

–

0 and 1, on and off, true or false

–

by using

simple transistors and capacitors.

transistor capacitor

Memory uses very small transistors and capacitors which can be

linked together to make simple logical calculations:

e.g

are

both inputs 1? or is only one input 1? These simple circuits are

called

Logic Gates.

GCSE

Computing#BristolMet

Logic Gates

There main gates are as follows:

1. NOT

gate

–

it outputs the opposite of the input

i.e

input =

1, then output = 0, and vice versa.

Truth Tables

are used to express the relationship between input

and output. (

Algebraic values are used, ABC

etc

for input and

PQR for output)

A

P

0

1

1

0

Input Output

GCSE

Computing#BristolMet

Logic Gates

2. AND

gate

–

this tells us if both inputs are 1 by outputting

1, otherwise the output will be 0

e.g

3. OR

gate

–

shows that either 1 OR 2 inputs are on by

outputting 1, otherwise output is 0.

e.g

A

B

P

0

0

0

0

1

0

1

0

0

1

1

1

A

B

P

0

0

0

0

1

1

1

0

1

1

1

1

GCSE

Computing#BristolMet

Logic Gate Diagrams

Each gate is represented by a different symbol:

NOT gate

AND gate

OR gate

INPUT

OUTPUT

GCSE

Computing#BristolMet

Logic Circuits

Logic gates can be joined together to make more complex

logic

circuits.

A common combination is the NAND circuit (Not AND) which

frustratingly is a AND followed by a NOT gate. Similarly a NOR

is an OR followed by a NOT.

NAND

–

basically toggles the AND so that if both inputs are 1

then 0 will be output, otherwise 1 is output.

Output R

Output P

A

B

R=

A AND B

P=NOT

R

0

0

0

1

0

1

0

1

1

0

0

1

1

1

1

0

GCSE

Computing#BristolMet

Logic Circuits

This example has 3 inputs, 2 in the AND (A&B), outputting to an

OR at P, and 1 directly into the OR.

The resulting truth table is calculated:

P

A

B

C

P=A AND B

Q = P OR C

0

0

0

0

0

0

0

1

0

1

0

1

0

0

0

0

1

1

0

1

1

0

0

0

0

1

0

1

0

1

1

1

0

1

1

1

1

1

1

1

GCSE

Computing#BristolMet

Boolean Algebra

These logic circuits can be written down using mathematical

expersions

called

Boolean

algebra (named after Mathematician

George Boole).

i.e

Q = (A AND B) OR C

TASKS

–

Draw logic circuits and truth tables for the following

愩

倽乏吨䄠䅎䐠䈩

戩

倽乏吨䄠佒O䈩

挩

P=A AND NOT (B)

搩

A AND NOT(B OR C)

GCSE

Computing#BristolMet

Boolean Programming

Boolean algebra is used in programming to perform many

instruction. For example IF statements and While loops

IF x >10 then...

ELSE....

__________________

WHILE x < 10 AND NOT (end of file) DO

Now try some simple programming using Ifs and Loops in

Yousrc

.

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