Transcript Kuliah 3(a)

Datum
Digitale basistechniek
lesplan
Theorie
Prakticum
Thuis
7 januari
Combinational Logic
Tutorial Quartus
II
Herhaling Tutorial
12 Januari
Combinational Logic
Halfadder
Fulladder
14 Januari
Functions of
Combinational Logic
2 bit decoder
BCDto7seg
19 Januari
Functions of
Combinational Logic
2-1 mux
1-2 demux
21 Januari
Flip-Flops and related
devices
Gated dlatch(8.3)
Example 8.12
26 Januari
Counters en
Statemachines
Frequency
divider8.11)
28 Januari
Counters en
Statemachines
4 bit synch
counter,
2 februari
Herhaling
Verkeerslicht 2
4 februari
Oefententamen
9 februari
Tentamen
verkeerslicht
Bepaling van het eindcijfer
• Het eindcijfer wordt bepaald door:
• 1 Voldoende Praktikum. (O/V)
• Tentamencijfer.
Introduction to Logic Gates
• Logical gates
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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
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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
Positive & Negative Logic
• 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
Positive & Negative Logic
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