# Logic Gates

LOGIC GATES

• Basic Logic Gates • Truth Tables • Logical Functions Truth Tables Logical Expression Graphical Form G hi l F

Most Difficult Reading Topics

• Logic gates and figuring out how to read them th • Logical Circuit Equivalence • NAND NOR and XOR truth tables • Using the rules to create and read the logic gates using 0's and 1's • Transistor implementation • Difference between positive logic and negative logic

Logic

• Formal logic is a branch of mathematics that deals th ti th t d l with true and false values instead of numbers. • In the mid-19th century, George Bool developed many Logic ideas. • Boolean logic deals with equations where the operators are “AND” or “OR” instead of “add” and “multiply”.

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Electric Logic

• Logical values can easily be expressed by an electrical circuit. l t i l i it • “True” or “1” can be defined as voltage on a wire while “False” or “0” can be defined as no voltage. We will use positive logic. • Analog values can be anything while digital only has discrete values, 0 or 1 • Electrical devices called “gates” can implement the logical

Logic Gates & Symbols

Note that gates can have more than 2 inputs.

AND gate

• The AND gate is an electronic circuit that gives a true output (1) only if all its inputs are true. A dot (·) is used to show the AND operation i.e. A·B. Note that the dot is sometimes omitted i.e. AB

Inputs and Outputs

• The inputs can be considered as logical (true or false) values. (t f l ) l • You can also think of the inputs as voltage (true) or ground (false). • The output of the gate will also be voltage (true) or ground (false) (false).

inputs

output

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OR gate

• The OR gate is an electronic circuit that gives a true output (1) if one or more of its inputs are true. A plus (+) is used to show the OR operation.

NOT gate

• The NOT gate is an electronic circuit that produces an inverted version of the input at its output. • It is also known as an inverter. • If the input variable is A, the inverted output is known as NOT A. • This is also shown as A', or Ā with a bar over the top A A’ 0 1 1 0

NAND gate

• This is a NOT-AND gate which is equal to t an AND gate followed by a NOT t f ll db gate. • The outputs of all NAND gates are true if any of the inputs are false. • The symbol is an AND gate with a small circle on the output. The small circle represents inversion.

NAND gate Cont.

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Logical Equivalence

• A NAND gate gives the same results as an AND gate feeding into a NOT gate. • Circuits are logically equivalent if they produce the same truth table output.

NAND as a NOT

• Below are two ways that a NAND gate can b configured to produce a NOT be fi dt d gate. They are logically equivalent. • It can also be done using NOR logic gates in the same way.

A 0 0 1 1

B AB NOT AB NAND AB 0 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0

A 0 1

A 0 1

NAND AA 1 0

A 0 1

1 1 1

NAND A’ 1 0

NOR gate

• This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate gate. • The outputs of all NOR gates are false if any of the inputs are true. • The symbol is an OR gate with a small circle on the output. The small circle represents inversion inversion.

NOR gate cont.

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EXOR gate

• The 'Exclusive-OR' gate is a circuit which will give a t ill i true output if either, but not t t ith b t t both, of its two inputs are true. • An encircled plus sign ( ) is used to show the EOR operation.

EXNOR gate

• The 'Exclusive-NOR' gate circuit does the th opposite t the EOR gate. it to th t • It will give a false output if either, but not both, of its two inputs are true. • The symbol is an EXOR gate with a small circle on the output output. • The small circle represents inversion.

EXNOR gate cont.

Logic gate symbols

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Truth Table

• Logic gates representation using the Truth table T th t bl

Try it

• Draw the circuit diagrams like the ones b l below t show how a NOR gate to h h t...

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