Transcript Building the CPU - Texas State Department of Computer Science

BUILDING THE CPU
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
control
unit
input/
output
registers
arithmeticlogic unit
Central Processing
Unit (CPU)
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 toggled
A relay is a switch built with an electromagnet
controlled current
controlling current
when the controlling current is 1, the electromagnet pulls
the switch closed, and the controlled current flows through
the switch
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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
in1
power
source
in1
in2
and
in2
out
when both inputs are 1,
the circuit is closed
out
= in1 in2
in1 in2 out
0 0
0
0 1
0
1
0
0
1
1
1
CS 302 - Computer Fluency
}
truth table
for AND
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Basic electric circuits:
Computing OR
in1
in2
out
when either input is 1,
the circuit is closed
in1
in2
or
in1 in2 out
0 0
0
0 1
1
out
1
0
1
1
1
= in1 + in2 1
}
truth table
for OR
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Basic electric circuits:
Computing NOT
in1
A new type of
switch
which is closed
at rest
in1
not
out
= in1’
in1 out
0 1
1 0
out
}
truth table
for NOT
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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
CS 302 - Computer Fluency
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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))
a
b
Value
0
0
1
0
1
0
1
0
0
1
1
1
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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
a
b
Output
0
0
1
0
1
0
1
0
0
1
1
1
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Figure 4.22
One-Bit Compare for Equality Circuit
CS 302 - Computer Fluency
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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
CS 1308 – Computer Literacy and the Internet
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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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