Logic Circuits Situations to explain states What is a logic Gate What 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 Homework done or homework not done Room cleared up and room not cleared up We know that the states will effect the output of going to the cinema or not

POSSIBLE OUTPUTS INPUTS DONE NOT DONE

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 OUTPUT INPUTS

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 Gate A single logic gate has the following attributes 1 or 2 inputs (if many gates are joined you could have more inputs ) 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 No 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 1

Comparing the two Truth Tables Homework Cleared Up Cinema Not Done No Done Yes Homework Cleared Up Cinema 1

Three Logic Gates We will now learn about three different logic gates We will be learning The symbol used The number of inputs Their truth tables The different outputs

The NOT Gate The 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 X 1

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 1 1 1 1

The OR Gate The symbol for the OR gate is the following; The OR gate can only have TWO inputs and ONE output A X B

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 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 Gate The symbol for the AND gate is the following; The AND gate can only have TWO inputs and ONE output A X B

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 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 Table Lets say we want to draw a truth table from the following logic circuit A B C

Step 1 Label 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 F E

Step 2 Determine 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 D A AND B E NOT C F D 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 D A AND B E NOT C F D OR E 1

Step 4 The last step is to work the resulting gates A B C D A AND B E NOT C F D OR E 1