Logic CircuitsSituations to explain states What is a logic GateWhat is a Truth Table The three different gates Building Truth Tables

Situation Lets say your friends have asked you to go

to the cinema with them but your mum will only allow you to go if you have finished your homework and cleared up your room.

In this situation we have the following states 1. Homework done or homework not done2. Room cleared up and room not cleared up

We know that the states will effect the output of going to the cinema or not

DONE

NOT DONE

POSSIBLEOUTPUTS

INPUTS

Example Taking the example of above; lets

say you’ve done your homework but you have not cleared up your room… what would the output be?

DONE

NOT DONE

OUTPUTINPUT

S

States So from the above example we could

see that the states effect the output that we will receive.

As we already know a computer can only understand binary which is 1s (on) and 0s (off)

Hence logic gates are used to be able to conduct similar situations

What is a Logic Gate Logic gates are found in our computers

They are electronic devices used to control the flow of data

When data passes through a logic gate it changes its state, this change depends on the input

Many logic gates could be joined together to form a logic circuit, the function of this circuit is more complicated than a single logic gate

A Single Logic GateA single logic gate has the

following attributes 1. 1 or 2 inputs (if many gates are

joined you could have more inputs )

2. 1 single output 1 input and 1 output

2 inputs and 1 output

What is a Truth Table A Truth Table is basically the

table that shows all the possible inputs and the outputs of the logic gate

If we take the example of the cinema once again we would have the following table Homework Cleared Up Cinema

Not Done Not Done NoNot Done Done NoDone Not Done NoDone Done Yes

Truth Tables As we know computers will not

understand the truth table on the previous page… why is this?

A truth table from an actual computerised logic gate would look like the following

Homework

Cleared Up

Cinema

0 0 00 1 01 0 01 1 1

Comparing the two Truth Tables

Homework Cleared Up Cinema Not Done Not Done NoNot Done Done NoDone Not Done NoDone Done Yes

Homework Cleared Up Cinema 0 0 00 1 01 0 01 1 1

Three Logic Gates We will now learn about three

different logic gates

We will be learning 1. The symbol used 2. The number of inputs3. Their truth tables 4. The different outputs

The NOT GateThe symbol for the NOT gate is

the following;

The NOT gate can only have ONE input and ONE output

A X

The NOT Gate Since computers only understand

1s and 0s there could be only two (21) possible inputs and outputs for this gate

The truth table shows this Input Output

A X0 11 0

Outputs The NOT gate basically outputs

the opposite of its inputs

Hence if the input is 1 the output would be 0

Example A good example is a switch as it

can either be on or off hence it can only have one input

01 1

01 0 0 1

The OR GateThe symbol for the OR gate is the

following;

The OR gate can only have TWO inputs and ONE output

A XB

The OR Gate Since computers only understand

1s and 0s there could be four (22) possible inputs and outputs for this gate

The truth table shows this Input OutputA B X0 0 00 1 11 0 11 1 1

Outputs The OR gate only gives an output

of 1 if at least one of its inputs is 1

So if both inputs are 0 the output would be 0

but if both inputs are 1 the output would be 1

Example

The AND GateThe symbol for the AND gate is

the following;

The AND gate can only have TWO inputs and ONE output

A XB

The OR Gate Since computers only understand

1s and 0s there could be four (22) possible inputs and outputs for this gate

The truth table shows this Input Output

A B X

0 0 0

0 1 0

1 0 0

1 1 1

Outputs The AND gate only gives an

output of 1 if both inputs are 1

So if an inputs 1 and the other input is 0 the output would be 0

but if both inputs are 1 the output would be 1

Example

Building a Truth TableLets say we want to draw a truth

table from the following logic circuit

A

B

C

Step 1Label all the possible outputs in

the logic circuit. In this case we have 3 inputs and there are 3 logic gates. Each logic gate’s output must be labeled;

D

E

F

Step 2Determine the possible number

of combinations. In this case it’s 23=8. So all the labels (both inputs and outputs are listed down with 8 spaces underneath each label).

A B C DA AND B

ENOT C

FD OR E

Step 3 Fill in the possible combinations

underneath the original inputs. Always start from the last input (C) with alternate 0s and 1s

A B C DA AND B

ENOT C

FD OR E

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

Step 4The last step is to work the

resulting gatesA B C D

A AND B

E

NOT C

F

D OR E

0 0 0 0 1 10 0 1 0 0 00 1 0 0 1 10 1 1 0 0 01 0 0 0 1 11 0 1 0 0 01 1 0 1 1 11 1 1 1 0 1