Binary Logic

OCR GCSE Computing

Starter

What is Binary Data?

Why is it important to represent data in a binary form?

Candidates should be able to:

d) explain why data is represented in computer systems in binary form

e) understand and produce simple logic diagrams using the operations NOT, AND and OR

f) produce a truth table from a given logic diagram.

Binary Logic

This is the process of using the computer to logically work through a sequence of instructions or problems

It helps the computer make a decision (output) based on a given input or inputs.

Is one OR the

other an Apple?

Apple

BananaYes

Logic Gates

There are a number of different logic gates that can be used to process data.

Thankfully we only need to know these three

AND OR NOT

Extension: Research other types of logic

gates

How they work

A logic gate accepts one or more binary inputs and produces one output.

The output will change depending on the type of gate that it is.

Look at the following slides for examples of different types of gates.

NOT

The NOT gate takes only one input and inverts it to create the output.

e.g.

If a 1 (on) value is sent as input a 0 (off) value if output as the result

0 1

AND

The AND Gate is slightly more complicated. It requires both inputs to be true (on) for the output to be true. Otherwise the output will be false (off)

0 01

000

100

111

OR

The OR Gate will produce a true (on) output whenever either or both of the input values are true (on)

0 11

000

110

111

Your goEnter the missing value from the logic gate

1

1

10

11

01

00

10

1

00

Combining Logic Gates

While useful by themselves logic gates become more useful when we join them together to create a logic diagram

01

11

How many different combinations of inputs are

there for this example?e.g. 0,0,0 0,0,1 0,1,0 0,1,1

Practical

An on/off switch (input)

And Gate

Or Gate

Not gate

Output Light

You will now attempt to create your own logic diagrams and test them to determine the output.

Goto www.neuroproductions.be/logic-lab/

Note that some diagrams look different. We will use the ones below

ActiviesCreate the diagram below and test it using the given inputs. Record the output

Both on

Top on bottom off

Both onTop on bottom off

Both off

ActivitiesCreate the diagram below and test it using the given inputs. Record the output

Both on

Top off bottom on

Both offTop on bottom off

Both on

ActivitiesCreate the diagram below and test it using the given inputs. Record the output

All onMiddle and Bottom OnTop On Bottom OnAll OffTop On

All onMiddle and Bottom OnTop On Middle OnAll Off

ActivitiesCreate the diagram below and test it using the given inputs. Record the output

All onMiddle and Bottom OnTop On Bottom OnMiddle and bottom OnAll Off

All onMiddle and Bottom OnTop On Middle OnTop OnAll Off

Activity

Draw each of the diagrams from earlier using the correct symbols

Design your own logic gates and create questions for others in the class to attempt.

Truth Tables

Another way of working out the output from a logic diagram without having to construct the circuit is by using a truth table

A truth table create a map of all of the different possible outcomes.

Note that:for one input there are two possible outcomes

for two inputs there are four possible outcomesfor three inputs there are eight possible outcomes

for four inputs there are _ _ _ _ _ _ _ possible outcomes

Truth Tables (AND)

First we want to label all of the inputs

AB

Next Create the table

A B A and B

Truth Tables (AND)

AB

Add the values For A

A B A and B

T

T

F

F

Truth Tables (AND)

AB

Add the values For B

A B A and B

T T

T F

F T

F F

Truth Tables (AND)

AB

Work out the operation. Always work from left to right if there is more than one logic gate

A B A and B

T T T

T F F

F T F

F F F

Truth Tables (OR)

First we want to label all of the inputs

AB

Next Create the table

A B A or B

Truth Tables (OR)

Add the values For A

A B A or B

T

T

F

F

AB

Truth Tables (OR)

Add the values For B

A B A or B

T T

T F

F T

F F

AB

Truth Tables (OR)

Work out the operation. Always work from left to right if there is more than one logic gate

A B A or B

T T T

T F T

F T T

F F F

AB

Truth Tables (NOT)

First we want to label all of the inputs

A

Next Create the table

A Not A

Truth Tables (NOT)

A

Add the values For A

A Not A

T

F

Truth Tables (NOT)

A

Add the values For Not A

A Not A

T F

F T

Multiple Logic GatesAB

C

A B C

Multiple Logic GatesAB

C

A B C D = A or B

Multiple Logic GatesAB

C

A B C D = A or B D and C

Multiple Logic GatesAB

C

A B C D = A or B D and C

T T T T T

T T F T F

T F T T T

T F F T F

F T T T T

F T F T F

F F T F F

F F F F F

Activities

Create truth tables for the earlier exercises

Plenary

Explain to a partner what each of the following terms means:

BinaryLogic

Truth TableLogic GateAND GateOR Gate

NOT Gate

Exam Questions