Transcript Digital Logic Circuit

Compiled by : Mr. Mark Anthony P. Cezar
( Lecture )
Chapter II
Introduction to Numeric and Binary System
Numbers(s)
A number is a mathematical object used to count and measure.
Classification of numbers
Natural Numbers
Integers
Rational Numbers
Complex Numbers
Computable Numbers
Binary Numeral System or Binary Number System
 Base-2 number system
Numeric values using two symbols 0 and 1
Used internally by almost all modern computers
Is a writing system of expressing numbers with symbol
The words binary comes from “Bi” MEANING TWO”
Example: Bicycle, Binocular
Example:
The number 10 means 2 in decimal
Why?
"There are 10 kinds of people in the world,
those who understand binary numbers, and
those who don't."
The BIT as a starting point . . . .
Bit is the smallest unit of data.
Where as, Binary Number is made up of only 0s and 1s
Number System Conversion
As computer programmer, it is important to know the different numeral system.
Same as . . .
BINARY ADDITION
BINARY SUBTRACTION
QUIZ
Addition
Subtraction
BINARY MULTIPLICATON
BINARY DIVISION
Binary Multiplication
1.
2.
3.
4.
5.
10 x 10 =
100 x 11 =
101 x 10=
1011 x 11 =
11011 x 101 =
Binary Division
1.
2.
3.
4.
5.
100 / 10 =
111 /11 =
1010/100 =
1101/11 =
101111 / 10 =
Answer Multiplication 1-5
Answer Division 1-5
MIND TEASER
Do not just think . .
.Analyze.
Know the logic . . …..
You have a fox, a chicken and a sack of
grain. You must cross a river with only one
of them at a time. If you leave the fox with
the chicken he will eat it; if you leave the
chicken with the grain he will eat it. How can
you get all three across safely?
Chapter II
Logic Circuits
Variables, functions, truth tables,
gates and networks
Digital Logic
 Logic Circuit used to build computer
Logic circuit perform operation on digital signals
The general form of logic circuit is a switching network
In binary Logic circuits are only two values 0 and 1
Digital Hardware
Late 1960s and early 1970s saw a revolutionary in digital capability
– smaller transistors
-larger chip size
More transistor/chip gives greater functionality
Integrated circuits are fabricated on silicon wafers
Chips have tens to million transistor
Provides motivation for computer based design techniques
15 Minutes
Review
quiz
1.z=tb+c
2.wxyx wy not(x) + wy
Quiz
Chapter III
Logic Circuits
Synthesis using AND, OR, and
NOT gates
Optimized Implementation of
Logic Functions:
Karnaugh Maps and Minimum
Sum-of-Product Forms
Example logic circuit design
• Assume we want to design a logic circuit with
three inputs x, y, and z
• The circuit output should be 1 only when x=1
and either y or z (or both) is 1
– Three possible combinations
• x=1, y=0, z=1 => xy’z
• x=1, y=1, z=0 => xyz’
• x=1, y=1, z=1 => xyz
• The function could be written as
– f(x,y,z)=xy’z+xyz’+xyz
Example logic circuit design
Karnaugh map
• The Karnaugh map (K-map) provides a
systematic (and graphical) way of performing
this operation
• Minterms can be combined by 14a when they
differ in only one variable
– f(x,y,z) = xyz+xyz’ = xy(z+z’) = xy(1) = xy
• The K-map illustrates this combination
graphically
Programmable logic devices, what are they?
Integrated circuit that you program using a hardware
description language such as VHDL or Verilog.
-Languages that you may have heard of are CUPL or ADA.
With the correct tools you can even generate a schematic
that is used to build the file that will be used to program the
device