Download Digital Logic Design

Digital Logic Design Ch1-1
Introduction to digital logic
(logic gates, flip-flops, circuits)
 Definition of Digital Logic
 Digital logic consists of binary variables and a set of
logical operations.
 The variables are designated by letters of the
alphabet, such as A, B, C, x, y, z, etc, with each
variable having two and only two distinct possible
values: 1 and 0,
Digital Logic Design Ch1-2
Logic Gates:
Digital systems are said to be constructed by using logic gates. These
gates are divided of three types of gate:
1- Basic gates:
AND gate
OR gate
NOT gate
2- Universal gates:
NAND gate
NOR gate
3- Derived gates:
EXOR gate
EXNOR gates.
Digital Logic Design Ch1-3
* AND gate
x
y
z
z=x•y=xy
x
y
z
0
0
0
0
1
0
1
0
0
1
1
1
The AND gate is an electronic circuit that gives
a high output (1) only if all its inputs are high. A dot (.) is
used to show the AND operation i.e. A.B.
Digital Logic Design Ch1-4
* OR gate
x
y
z
z=x+y
x
y
z
0
0
0
0
1
1
1
0
1
1
1
1
The OR gate is an electronic circuit that gives a high
output (1) if one or more of its inputs are high. A
plus (+) is used to show the OR operation
Digital Logic Design Ch1-5
* NOT gate
x
z
X =Z=X
x
z
0
1
1
0
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 A
with a bar over the top.
Digital Logic Design Ch1-6
Switching Circuits
Representing AND Gate by Electric Circuit
off
on
on
off
SW1
SW2
on
off
SW1
SW2
Lamp
Lamp
Digital Logic Design Ch1-7
Switching Circuits
Representing OR Gate by Electric Circuit
off
on
SW1
on
off
off
on
SW1
SW2
Lamp
SW2
Lamp
Digital Logic Design Ch1-8
Switching Circuits
Representing NOT Gate by Electric Circuit
on
off
SW
SW
Lamp
on
off
Lamp
Digital Logic Design Ch1-9
Binary Logic
 Logic gates

Example of binary signals
3
Logic 1
2
Un-define
1
Logic 0
0
Figure 1.3 Example of binary signals
Digital Logic Design Ch1-10
Binary Logic
 Logic gates

Graphic Symbols and Input-Output Signals for Logic gates:
Fig. 1.4 Symbols for digital logic circuits
Fig. 1.5 Input-Output signals for gates
Digital Logic Design Ch1-11
In Put
The NAND gate represents the
complement of the AND operation.
Its name is an abbreviation of NOT
AND.
Out Put
X
Y
Z
0
0
1
0
1
1
0
1
1
1
1
0
𝑍 = 𝑋. 𝑌
Digital Logic Design Ch1-12
In Put
The NOR gate represents the
complement of the OR operation.
Its name is an abbreviation of NOT
OR.
Out Put
X
Y
Z
0
0
1
0
1
1
0
0
0
1
1
0
𝑍 =𝑋+𝑌
Digital Logic Design Ch1-13
In Put
The output is high when either of
inputs A or B is high, but not if
both A and B are high. It is consists
of a five gates (two AND, two
NOT, and one OR)
Out Put
A
B
F
0
0
0
0
1
1
0
1
1
1
1
0
𝐹 = 𝐴⨁𝐵
Digital Logic Design Ch1-14
In Put
This is an X-OR gate with the
output inverted. It is consists of a
five gates (two AND, two NOT,
and one OR)
Out Put
A
B
F
0
0
1
0
1
1
0
0
0
1
1
1
𝐹 = 𝐴⨂𝐵
F=𝐴⨁𝐵
Digital Logic Design Ch1-15
More about logic gates
 To implement a logic gate in hardware, you use a transistor
 Transistors are all enclosed in an “IC”, or integrated circuit
 The current Intel Pentium IV processors have 55 million
transistors!
16 Logic Design Ch1-16
Digital
Flip-Flops and Digital Circuits
Digital Logic Design Ch1-17
 A digital circuit that contains flip-flops is called a
Sequential Circuit
 A flip-flop holds a single bit of memory
The bit “flip-flops” between the two NAND gates
 In reality, flip-flops are a bit more complicated
Have 5 (or so) logic gates (transistors) per flipflop
Digital Logic Design Ch1-18
1- R-S flip-flop
R
S
2- D flip-flop
3- J-K flip-flops
Digital Logic Design Ch1-19
Flip-flops
 R-S Flip-Flope Consider the
following circuit:
R
S
Q
Q
R
S
Function
1
0
Reset
0
1
Set
1
1
Hold
0
0
1/1
holds it’s a single bit of memory.
20 Logic Design Ch1-20
Digital