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ReviewCPSC 321
Andreas Klappenecker
Administrative Issues
• Midterm is on October 12• Allen Parish’s help session Friday 10:15-
12:15
Questions? Project partners?
Today’s Menu
What happened so far...
History
One of the first calculation tools was the abacus, presumably invented sometime between 1000-500 B.C.
Early History
• around 1600, John Napier invents the Napier bones, a tool that helps in calculations
• 1621, William Oughtred invents the slide rule that exploit Napier’s logarithms to assist in calculations
• 1625 Wilhelm Schickard invents a mechanical device to add, subtract, multiply and divide numbers
• 1640 Blaise Pascal invents his Arithmetic Machine (which could only add)
• 1671 Wilhelm von Leibniz invents the Step Reckoner, a device that allows to perform additions, subtractions, multiplications, divisions, and evaluation of square roots (by stepped additions)
Early History
• Charles Babbage proposes in 1822 a machine to calculate tables for logarithms and trigonometric functions, called the Difference Engine.
• Before completing the machine, he invents in 1833 the more sophisticated Analytic Engine that uses Jacquard punch cards to control the arithmetic calculations• The machine is programmable, has storage capabilities, and
control flow mechanisms – it is a general purpose computer.• The Analytic Engine was never completed.
• Augusta Ada Lovelace writes the first program for the Analytical Engine (to calculate Bernoulli numbers). Some consider her as the first programmer.
Z1
The Z1 computer was clocked at 1 Hz. The memory consists of 64 words with 22 bits. Input and output is done by a punch tape reader and a punch tape writer. The computer has two registers with 22 bits and is able to perform additions and subtractions (it is not a general purpose computer).
Z3
Zuse constructed the Z3, a fully programmable general purpose computer, in 1939-1941. Remarkably, it contained a binary floating point arithmetic. It was clocked at 5.33 Hz, based on relays, and had 64 words of 22 bits. The small memory did not allow for storage of the program.
(Art and photo courtesy of Horst Zuse)
Performance
• Response time: time between start and finish of the task (aka execution time)
• Throughput: total amount of work done in a given time
Performance
Relative Performance
(Absolute) Performance
Amdahl’s Law
The execution time after making an improvement to the system is given by
Exec time after improvement = I/A + E
I = execution time affected by improvementA = amount of improvementE = execution time unaffected
Assembly Language
.text # code section
.globl main
main: li $v0, 4 # system call for print string
la $a0, str # load address of string to print
syscall # print the string
li $v0, 10 # system call for exit
syscall # exit
.data
str: .asciiz “Hello world!\n” # NUL terminated string, as in C
Things to know...
• Instruction and pseudo-instructions• Register conventions (strictly
enforced)• Machine language instruction given,
find the corresponding assembly language instruction
• Code puzzles • Solve a small programming task
Instruction Word Formats
• Register format
• Immediate format
• Jump format
op-code rs rt rd shamt functop-code rs rt rd shamt funct
op-code rs rt immediate valueop-code rs rt immediate value
op-code 26 bit current segment addressop-code 26 bit current segment address
6 5 5 16
6 5 5 5 5 6
6 26
Machine Language
• Machine language level programming means that we have to provide the bit encodings for the instructions
• For example, add $t0, $s1, $s2 represents the 32bit string
• 00000010001100100100000000100000• Assembly language mnemonics usually
translate into one instruction• We also have pseudo-instructions that
translate into several instructions
What does that
mean?
Watson, the case is clear…
• add $t0, $s1, $s2• 00000010001100100100000000100000
• 000000 10001 10010 01000 00000 100000• Operation and function field tell the computer to
perform an addition
• 000000 10001 10010 01000 00000 100000• registers $17, $18 and $8
op-code rs rt rd shamt functop-code rs rt rd shamt funct
6 5 5 5 5 6
Number Representations
• Signed and unsigned integers• Number conversions• Comparisons• Overflow rules
• No overflow when adding a positive and a negative number
• No overflow when signs are the same for subtraction
• Overflow occurs when the value affects the sign:• overflow when adding two positives yields a negative • or, adding two negatives gives a positive• or, subtract a negative from a positive and get a
negative• or, subtract a positive from a negative and get a positive
Detecting Overflow
Detecting Overflow
Operation
Operand A
Operand B
Overflow if result
A+B >=0 >=0 <0
A+B <0 <0 >=0
A-B >=0 <0 <0
A-B <0 >=0 >=0
Logic Design: Build ALU, etc.
Result31a31
b31
Result0
CarryIn
a0
b0
Result1a1
b1
Result2a2
b2
Operation
ALU0
CarryIn
CarryOut
ALU1
CarryIn
CarryOut
ALU2
CarryIn
CarryOut
ALU31
CarryIn
b
0
2
Result
Operation
a
1
CarryIn
CarryOut
Logic Design
• Determine truth tables of combinatorial circuits
• Determine combinatorial circuits from truth tables
• Determine critical path• Overflow detection in ALU
SLT
0
3
Result
Operation
a
1
CarryIn
CarryOut
0
1
Binvert
b 2
Less
0
3
Result
Operation
a
1
CarryIn
0
1
Binvert
b 2
Less
Set
Overflowdetection
Overflow
a.
b.
• 4 operations• subtraction output available• Connect • MSB set output
w/ LSB less
Adders
• Ripple carry• Carry-lookahead
Fast Adders
Iterate the idea, generate and propagateci+1 = gi + pici
= gi + pi(gi-1 + pi-1 ci-1)
= gi + pigi-1+ pipi-1ci-1
= gi + pigi-1+ pipi-1gi-2 +…+ pipi-1 …p1g0
+pipi-1 …p1p0c0
Two level AND-OR circuit Carry is known early!
Multiplication
Done
1. TestMultiplier0
1a. Add multiplicand to product andplace the result in Product register
2. Shift the Multiplicand register left 1 bit
3. Shift the Multiplier register right 1 bit
32nd repetition?
Start
Multiplier0 = 0Multiplier0 = 1
No: < 32 repetitions
Yes: 32 repetitions
64-bit ALU
Control test
MultiplierShift right
ProductWrite
MultiplicandShift left
64 bits
64 bits
32 bits
0010 (multiplicand)__ x_1011 (multiplier) 0010 x 1 00100 x 1
001000 x 0 0010000 x 1
0010110
Booth Multiplication
Current and previous bit
00: middle of run of 0s, no action01: end of a run of 1s, add multiplicand10: beginning of a run of 1s, subtract
mcnd11: middle of string of 1s, no action
Example: 0010 x 0110
Iteration
Mcand
Step Product
0 0010 Initial values 0000 0110,0
1 0010 0010
00: no op arith>> 1
0000 0110,0
0000 0011,0
2 0010 0010
10: prod-=Mcandarith>> 1
1110 0011,0 1111 0001,1
3 0010 0010
11: no oparith>> 1
1111 0001,1 1111 1000,1
4 0010
0010
01: prod+=Mcandarith>> 1
0001 1000,1 0000 1100,0
IEEE 754 Floating Point Representation
• Float – 1 sign bit, 8 exponent bits, 23 bits for significand.
seeeeeeeefffffffffffffffffffffffvalue = (-1)s x F x 2E-127
with F= 1 + .ffffffff .... fff
• Double – 1 sign bit, 11 exponent bits, 52 bits for significand
Processor
• Be able to build the datapath• Be able to explain issues concerning
datapath and control
Control
PC
Instructionmemory
Readaddress
Instruction[31– 0]
Instruction [20– 16]
Instruction [25– 21]
Add
Instruction [5– 0]
MemtoReg
ALUOp
MemWrite
RegWrite
MemRead
BranchRegDst
ALUSrc
Instruction [31– 26]
4
16 32Instruction [15– 0]
0
0Mux
0
1
Control
Add ALUresult
Mux
0
1
RegistersWriteregister
Writedata
Readdata 1
Readdata 2
Readregister 1
Readregister 2
Signextend
Shiftleft 2
Mux
1
ALUresult
Zero
Datamemory
Writedata
Readdata
Mux
1
Instruction [15– 11]
ALUcontrol
ALUAddress
Single- versus Multicycle Processor
• What are the differences? • What is executed during the 7th
cycle?• How many cycles do we need?
Summary
Step nameAction for R-type
instructionsAction for memory-reference
instructionsAction for branches
Action for jumps
Instruction fetch IR = Memory[PC]PC = PC + 4
Instruction A = Reg [IR[25-21]]decode/register fetch B = Reg [IR[20-16]]
ALUOut = PC + (sign-extend (IR[15-0]) << 2)
Execution, address ALUOut = A op B ALUOut = A + sign-extend if (A ==B) then PC = PC [31-28] IIcomputation, branch/ (IR[15-0]) PC = ALUOut (IR[25-0]<<2)jump completion
Memory access or R-type Reg [IR[15-11]] = Load: MDR = Memory[ALUOut]completion ALUOut or
Store: Memory [ALUOut] = B
Memory read completion Load: Reg[IR[20-16]] = MDR
Need for Speed
• You need to be able to answer the question in a short time (75 minutes)
• Routine calculations, such as number conversions, should not slow you down
• Read the chapters very carefully!• Many repetitions will help you to gain
a better understanding
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