Logic Gates

Binary Logic/Boolean Logic (definition)

The process of reducing values to either True or False, in order to perform calculations.

Logic Gate (definition)

A building block of the digital circuitry found in a CPU. It performs a logical operation on the inputs it receives.

What is a logic circuit?

A combination of logic gates which are used to process data.

AND gate

Both A and B need to be True, otherwise its false

AND gate notation

A ^ B /A.B/ AB/A AND B

Draw an AND gate in Sketchbook

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OR gate

True if A or B or both is True, otherwise its False

OR gate notation

A V B / A+B /A OR B

Draw an OR gate

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NOT Gate

True when A is False. Opposite day

NOT Gate notation

¬A/~A/Ā/!A

Draw a NOT Gate

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NAND Gate

True if only A and B are false, otherwise it’s False

NAND Notation

¬(A^B)/A | B/A ↑ B/A NAND B

Draw a NAND Gate

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NOR Gate

True if A or B or both are False, otherwise it’s False

Draw a NOR Gate

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What is a XOR gate

True when A or B but not both are True

XOR Notation

A ⊻ B. A⊕B. A XOR B

Draw a diagram of an XOR gate

What is a XNOR Gate?

True when A or B but not both are False

Draw a diagram of an XNOR gate

XNOR Notation (2)

A↔B. A≡B

Order of Precedence of Boolean Alegbra

Brackets. NOT. AND. OR

Function of a half adder

Adds two single-bit binary numbers

What is the sum?

Result of adding bits

What is the carry?

Carries to next stage if both are 1

Function of a full adder

Same as a half adder but includes a carry-in from a previous addition

Differences between half adder and full adder (Half-adder)

Two inputs. Cannot handle a carry from a previous stage. Adds two single bits only. Simpler circuit

Differences between half adder and full adder (Full-adder)

Three inputs. Can handle a carry in from a previous stage. Adds three bits. More complex circuits