fall 2012: fcm 708 foundation i lecture 2 prof. shamik sengupta email: [email protected]
TRANSCRIPT
Fall 2012: FCM 708 Fall 2012: FCM 708 Foundation IFoundation I
Lecture 2Lecture 2
Prof. Shamik Sengupta
Email: [email protected]
Quick Recap…
Intro to Computer Architecture:
– Number system– Decimal, Binary, Hexadecimal
– Unsigned and signed representations
– Hardware architecture– A simplified model of the microprocessor structure
– Central Processing Unit (CPU)
– Arithmetic & Logic Unit (ALU)
– Control Unit (CU)
– Register Array
– System Bus
– Memory
– Overview of Instruction Execution Cycle
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A quick look at a microprocessor architecture
Let us have some hand-on experience of what we have learnt so far
We will use a simple microprocessor simulator– Motorola 68HC11
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Boolean algebra and Logic gatesBoolean algebra and Logic gates
Objectives
Understand the relationship between Boolean logic
and digital computer circuits
Learn how to design simple logic circuits.
Understand how digital circuits work together to form
complex computer systems.
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Introduction
In the latter part of the nineteenth century, George Boole showed that logical thought could be represented through mathematical equations
Computers, as we know them today, are implementations of Boole’s Laws of Thought– John Atanasoff and Claude Shannon were among the first to see
this connection
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What is Boolean algebra
Boolean algebra is an algebra for the manipulation of objects that can take on only two values, typically true and false
Why Boolean algebra is so useful in computers?– Because computers are built as collections of gates that are either “on”
or “off,” Boolean algebra is a very natural way to represent digital information or compute information
Boolean functions are implemented in digital computer circuits called gates (logic gates)– A gate is an electronic device that produces a result based on two or
more input values– All the microprocessor components are combinations of such logic gates
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Boolean Operators
Most common Boolean operators are AND, OR and NOT
A Boolean operator can be completely described using a truth table
The truth table for the Boolean operators AND, OR and NOT are shown here
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The three simplest gates are the AND, OR, and NOT gates.
They correspond directly to their respective Boolean operations, as you can see by their truth tables
And these representations map exactly into the electric circuits of a digital system
Logic Gates
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Detailed implementation picture of a Logic Gate
Voltage inverted from input
Voltage from input
This is the logic for an AND gate
74LS08Quad 2-input AND
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The output of the XOR operation is true only when the values of the inputs differ.
Logic Gates
Note the special symbol for the XOR operation. • Symbols for NAND and NOR, and
truth tables are shown at the right.
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Three other logic gates:
Logic Gates
NAND is known as universal gate because they are inexpensive to manufacture and any Boolean function can be constructed using only NAND gates.
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Boolean Functions
Boolean functions are composed of Boolean variables and multiple logic operators
NOT has the precedence over AND AND has the precedence over OR
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Boolean Functions
Digital computers contain circuits that implement Boolean functions.
The simpler that we can make a Boolean function, the smaller the circuit that will result.– Simpler circuits are cheaper to build, consume less power,
and run faster than complex circuits.
With this in mind, we always want to reduce our Boolean functions to their simplest form.– Boolean identities
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Most Boolean identities have an AND (product) form as well as an OR (sum) form.
We show our identities using both forms. Our first group is rather intuitive:
Boolean identities
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Our second group of Boolean identities should be familiar to you from your study of algebra:
Boolean identities
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Our last group of Boolean identities are perhaps the most useful.
Boolean identities
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Simplification of Boolean Functions
Let’s try some of these identities to simplify Boolean Functions:
F = AB + BBC + BCC
F = A + B(A+C) + AC
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Simplify the function:
Simplification of Boolean Functions
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Hand-on Practice
Multimedia Logic Simulator
Can be downloaded from http://www.softronix.com/logic.html
We will implement some of the simplest logic circuits
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Digital Circuits and Boolean Algebra
Using Boolean algebra to design various important digital circuits implementation
– Designing a Burglar alarm
– Designing an adder
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Reading Assignment
1. Boolean Algebra (In Blackboard)
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