OCR GCSE Computing

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2 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

115 εμφανίσεις

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



倽乏吨䄠䅎䐠䈩


倽乏吨䄠佒O䈩


P=A AND NOT (B)


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
.