Digital Logic Circuit Chapter

Chapter V
Digital Logic Circuit
Intr. to Mechatronics Prepare by: Bereket 1

5. Digital Logic
Introduction:
• Digital electronic devices used for logic, display, sequencing, timing, and
other functions in mechatronic systems.
• The fundamentals presented in this chapter are important in understanding the
basic functioning of all digital components and systems used in the control of
mechatronic systems.
• Analog signal that changes in a continuous manner, a digital signal exists
only at specific levels or states and changes its level in discrete steps.
• Most digital signals have only two states: high and low.
• A system using two-state signals allows the application of Boolean logic and
binary number representations,
• which form the foundation for the design of all digital devices

5. Digital Logic
• Digital devices are categorized according to their function as combinational
logic or sequential logic devices.
Combinational Logic Circuit
• Combinational Logic circuit contains logic gates where its output is
determined by the combination of the current input, regardless of the output
or the prior combination of input.
• Basically, combinational circuit can be depicted by Diagram 1 below:
• Digital devices convert digital inputs into one or more digital outputs.
• The difference between the two categories is based on signal timing.

5. Digital Logic
• Logic circuits for half adder (HA)

5. Digital Logic
Sequential Logic Circuit
• Sequential Logic Circuit contains logic gates arranged in parallel and its output
is not only determined by the combination of the current input, but also the
prior output.
• The circuit also contains memory elements that enable it to store the
information of the prior output.
• Examples of sequential circuits in the computer system are like registers,
counters and serial adders

5. Digital Logic
Gated S/R Latch

5. Digital Logic
• The standard AND, NAND, OR, NOR, and XOR gates have only two inputs,
but other forms are available with more than two inputs.
• In the case of a multiple input AND gate, the output is 1 if and only if all
inputs are 1.
• Logic gates are built using transistors

NOT Gate -- Inverter
X Y
0
1
1
0
X Y
Y
NOT
X Y
Y = ~X
NOT

NOT
X ~X ~~X = X
X ~X ~~X
0 1 0
1 0 1

AND Gate
AND
X
Y
Z
Z = X & Y
X Y Z
0 0 0
0 1 0
1 0 0
1 1 1

OR Gate
OR
X
Y
Z
Z = X | Y
X Y Z
0 0 0
0 1 1
1 0 1
1 1 1

NAND Gate
NAND
X
Y
Z
X Y Z
0 0 1
0 1 1
1 0 1
1 1 0
Z = ~(X & Y)
nand(Z,X,Y)

NAND Gate
NOT-AND
X
Y
Z
W = X & Y
Z = ~W = ~(X & Y)
X Y W Z
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
W

NOR Gate
NOR
X
Y
Z
X Y Z
0 0 1
0 1 0
1 0 0
1 1 0
Z = ~(X | Y)
nor(Z,X,Y)

NOR Gate
NOT-OR
X
Y
W = X | Y
Z = ~W = ~(X | Y)
X Y W Z
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0
Z
W

Exclusive-OR Gate
X Y Z
XOR
X
Y
Z 0 0 0
0 1 1
1 0 1
1 1 0
Z = X ^ Y
xor(Z,X,Y)

Exclusive-NOR Gate
X Y Z
XNOR
X
Y
Z 0 0 1
0 1 0
1 0 0
1 1 1
Z = ~(X ^ Y)
Z = X ~^ Y
xnor(Z,X,Y)

5. Digital Logic
Note: The algebraic symbols used to represent the logic functions are: plus (+) for
logic OR, dot (·) for the logic AND, and an overbar for logic NOT, denoting inversion.

5. Digital Logic

5. Digital Logic
Timing diagrams

5. Digital Logic
Boolean algebra

5. Digital Logic
Logical Expression Simplification
Note: K-map method take it as reading assignment

5. Digital Logic

5. Digital Logic
• NAND and NOR gates are called universal gate

5. Digital Logic
• Logic Chips are built from logic gates
• Integration levels may be Small(SSI), Medium(MSI), Large(LSI) or
Very Large Scale Integration (VLSI).

5. Digital Logic
Draw the Circuit Diagram

End of Chapter V

Digital Logic Circuit Chapter

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