cs 1308 – computer literacy and the internet. it’s not magic the goal of the next series of...
TRANSCRIPT
CS 1308 – Computer Literacy and the Internet
It’s Not Magic
The goal of the next series of lectures is to show you exactly how a computer works.
We will discuss the logic used to create computer instructions and how the computer decides which instructions to execute.
Although at times it may appear to be magical. It’s just math and science.
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Our Picture of a Computer
Data Bus
memory input/ output
controlunit
arithmetic-logic unit
Central ProcessingUnit (CPU)
registers
The Reliability of Binary Representation
Electronic devices are most reliable in a bistable environment
Bistable environment Distinguishing only two electronic states
Current flowing or not
Direction of flow
Computers are bistable: hence binary representations
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A Switch is a 2-state device that can be toggledA relay is a switch built with an
electromagnet
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controlled current
controlling current
when the controlling current is 1, the electromagnet pullsthe switch closed, and the controlled current flows through
the switch
Switches can do it all
With switches we can implement AND, OR, and NOT gates
With just those types of gates, we can design circuits to perform any computation
Remember, computers do very simple tasks, very quickly
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Basic electric circuits:
Computing AND
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in1 in2 out 0 0 0 0 1 0 1 0 0 1 1 1
truth table for AND}
when both inputs are 1,the circuit is closed
andin1in2 out
= in1 in2
outpowersource
in1 in2
Basic electric circuits:
Computing OR
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in1 in2 out 0 0 0 0 1 1 1 0 1 1 1 1
truth table for OR}in1
in2 outor
= in1 + in2
out
in1
in2
when either input is 1,the circuit is closed
Basic electric circuits:
Computing NOT
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in1 out 0 1 1 0
truth table for NOT}
A new type of switch
which is closedat rest
in1 out
= in1’
not
out
in1
A better switch: Transistors
bi-stable, solid state device switching is done electronically, not
mechanically no moving parts; therefore, fast, small,
reliable can switch states in about one 10 billionth of a
second about 5 million transistors can fit on a chip 1
centimeter square. Density is increasing rapidly with new technology.
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Figure 4.11
Simplified Model of a Transistor
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Boolean Logic and Gates: Boolean Logic
Boolean logic describes operations on true/false values
True/false maps easily onto bistable environment
Boolean logic operations on electronic signals may be built out of transistors and other electronic devices
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Boolean Logic (continued) Boolean expressions
Constructed by combining together Boolean operations
Example: (a AND b) OR ((NOT b) AND (NOT a))
Truth tables capture the output/value of a Boolean expression
A column for each input plus the output
A row for each combination of input values
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Boolean Logic (continued) Example:
(a AND b) OR ((NOT b) and (NOT a))
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a b Value
0 0 1
0 1 0
1 0 0
1 1 1
Building Computer Circuits: Introduction
A circuit is a collection of logic gates:
Transforms a set of binary inputs into a set of binary outputs
Values of the outputs depend only on the current values of the inputs
Combinational circuits have no cycles in them (no outputs feed back into their own inputs)
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A Compare-for-equality Circuit Compare-for-equality circuit
CE compares two unsigned binary integers for equality
Built by combining together 1-bit comparison circuits (1-CE)
Integers are equal if corresponding bits are equal (AND together 1-CD circuits for each pair of bits)
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A Compare-for-equality Circuit (continued)
1-CE circuit truth table
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a b Output
0 0 1
0 1 0
1 0 0
1 1 1
Figure 4.22
One-Bit Compare for Equality Circuit
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A Compare-for-equality Circuit (continued)
1-CE Boolean expression
First case: (NOT a) AND (NOT b)
Second case: a AND b
Combined:
((NOT a) AND (NOT b)) OR (a AND b)
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Examples Of Circuit Design And Construction
Compare-for-equality circuit
Addition circuit
Both circuits can be built using the sum-of-products algorithm
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An Addition Circuit
Addition circuit
Adds two unsigned binary integers, setting output bits and an overflow
Built from 1-bit adders (1-ADD)
Starting with rightmost bits, each pair produces
A value for that order
A carry bit for next place to the left
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An Addition Circuit (continued) 1-ADD truth table
Input
One bit from each input integer
One carry bit (always zero for rightmost bit)
Output
One bit for output place value
One “carry” bit
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Figure 4.24
The 1-ADD Circuit and Truth Table
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An Addition Circuit (continued) Building the full adder
Put rightmost bits into 1-ADD, with zero for the input carry
Send 1-ADD’s output value to output, and put its carry value as input to 1-ADD for next bits to left
Repeat process for all bits
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Computer Instructions
The logic for every instruction is executed on every cycle by the Arithmetic and Logic Unit (ALU).
The answer used is the one for the instruction that is currently decoded and executed by the CPU.
This selection is done by the Control Circuits.
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Control Circuits
Do not perform computations Choose order of operations or select among
data values described by the instruction The pattern of ones and zeros in each
instruction will determine the which result is used from the ALU
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Control Circuits (cont.)
Major types of controls circuits Multiplexors
Select one of inputs to send to output
Decoders Sends a 1 on one output line, based on
what input line indicates
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Summary
Binary values create a bistable environment, making computers reliable
Boolean logic maps easily onto electronic hardware
Circuits are constructed using Boolean expressions as an abstraction
Computational and control circuits may be built from Boolean gates
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