Logic Gates

1MOHD. YAMANI IDRIS/ NOORZAILY MOHAMED NOOR
Introduction to Logic Gates
• Logical gates
– Inverter
– AND
– OR
– NAND
– NOR
– Exclusive OR (XOR)
– Exclusive NOR (XNOR)
• Draw Logic Circuit
• Analysis of Logic Circuit

Introduction to Logic Gates
• Universal gates NAND and NOR
– NAND gate
– NOR gate
• Execution using NAND gate
• Execution using NOR gate
• Positive & Negative Logic
• SOP Expression Execution
• POS Expression Execution
• Integrated Logic Circuit Family

Logic Gates

Logic Gates
• Inverter gate
• The use of inverter: complement

Logic Gates
• AND gate

Logic Gates
• OR gate

Logic Gates
• NAND gate

Logic Gates
• NOR gate

Logic Gates
• Exclusive OR (XOR) gate

Logic Gates
• Exclusive NOR (XNOR) gate

Draw Logic Gates
• When Boolean expression is obtained, we
can draw logic gates
• Example:
– F1 = xyz’ (use three input AND gate)

Draw Logic Gates

Logic Circuit Analysis
• When logic circuit is given, we can analyze
the circuit to obtain logical expression
• Example:
– What is the Boolean expression for F4

Logic Circuit Analysis
• What is the Boolean expression for F5

Universal Gates: NAND & NOR
• Gate AND/OR/NOT is enough to build any
Boolean function
• Even though, other gates is also used because:
– Very useful (no choice)
– Save transistor’s number
– Self sufficient (can build any gate from it)
NAND/NOR: save, self sufficient
XOR: useful (e.g. execute parity bit)

NAND Gate
• NAND gate is self sufficient (i.e.can build
any gate from it)
• Can be used for building AND/OR/NOT
gate
• Build NOT gate using NAND gate

NAND Gate
• Build AND gate using NAND gates
• Build OR gate using NAND gates

NOR Gate
• NOR gate is also self sufficient
• Can be used for building AND/OR/NOT
gate
• Build NOT gate using NOR gate

NOR Gate
• Build AND gate using NOR gates
• Build OR gate using NOR gates

Build using NAND gate
• It is not impossible to build Boolean
expression using NAND gates
Steps
– Obtain sum-of-product Boolean expression
• E.g: F3 = xy’ +x’z
– Use DeMorgan theorem to get expression using
two level NAND gate
• E.g: F3 = xy’ +x’z
= (xy’+x’z)”
= ((xy’)’.(x’z)’)’

Build using NAND gate

Build using NOR gate
• It is not impossible to build Boolean
expression using NOR gates
Steps
– Obtain product-of-sum Boolean expression
• E.g: F6 = (x+y’).(x’+z)
– Use DeMorgan theorem to get expression using
two level NAND gate
• E.g: F3 = (x+y’).(x’+z)
=((x+y’).(x’+z))’’
= ((x+y’)+(x’+z)’)’

Build using NOR gate

Positive & Negative Logic
• In logic gate, most of the time
– H (High Voltage, 5V) = logic 1
– L (Low Voltage, 0V) = logic 0
• This is called positive logic
• However, if it is inverted, it is negative logic
– H (High Voltage, 5V) = logic 0
– L (Low Voltage, 0V) = logic 1
• Depends, some similar gate need different
Boolean function

• Signal which is set to logic 1 is said to be
active and true
• Signal which is set to logic 0 is said to be
not active and false
• The name of active high signal is always
written in non-compliment form
• The name of active low signal is always
written in non-compliment form

Construction of SOP Expression
• Sum-of-product expression can be built
using
– Two level logic gate AND-OR
– Two level logic gate AND-NOT
• Logic AND-OR gate

Construction of SOP Expression
• NAND-NAND circuit (with transformation
circuit)
– Add two balls
– Change OR with NAND
with inverted input and ball
on it’s compliment input

Construction of POS Expression
• Product-of-sum expression can be built
using
– Two level logic gate AND-OR
– Two level logic gate AND-NOT
• Logic AND-OR gate

Construction of POS Expression
• NOR-NOR circuit (with transformation
circuit)
– Add two balls
– Change AND with NOR
with inverted input and ball
on it’s compliment input

”:

Logic Gates

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