1. Part II : Lecture III
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2. Multiplication 0010 (multiplicand) x 1011 (multiplier) ????
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3. Unsign Combinational Multiplier
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4. Multiplication : First Version (Unsign)
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5. Multiplication : First Version (contd.)
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6. Analyze First Version 1 clock per cycle
50 % of bit in multiplicand always = 0
=> 64-bit adder is wasted
0’s inserted in left of multiplicand as shifted
=> lead significant bits of product never changed once formed
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7. Multiplication : Second Version
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8. Multiplication : Second Version (Contd.)
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9. Analyze Second Version
Product register wasted space that exactly matches size of multiplier
Combine Multiplier register and Product register
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10. Multiplication : Third Version
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11. Multiplication : Third Version (Contd.)
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12. Analyze Third Version
2 steps per bit because multiplier & product combined
MIPS registers Hi, Lo are left and right half of product
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13. Booth’s Algorithm
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14. Example : 2 x 7
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15. Example : 2 x -3
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16. Shifter : 2 kinds
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17. Part III : Lecture III
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18. Divide
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19. Divide : First Version
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20. Divide : First Version (Contd.)
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21. Analyze First Version 50% bits in divisor always 0
=>1/2 of 64-bit adder is wasted
=> 1/2 divisor is wasted
1 step cannot produce a 1 in quotient bit
=> Switch order to shift first
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22. Divide : Second Version
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23. Divide : Second Version (Contd.)
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24. Analyze Second Version
Eliminate Quotient register by combining with Remainder as shifted left
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25. Divide : Third Version
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26. Divide : Third Version (Contd.)
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27. Analyze Third Version
Do Analyze by yourself
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28. Floating Point : IEEE754
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29. Floating-point Representation
-0.75
= -3/4 = -3/22
= -11/ 22 = = -1.1x 2-1
= (-1)s x (1 + signifiand) x 2 (exponent-127)
= (-1) x ( ) x 2( )
S E M
1-bit 8-bit bit
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30. Floating-point Addition
9.999 x x10-1
Step1 : Change exponent as :
1.610 x = x 101
Step2 : Add significands
9.999 (10)
(10)
(10)
Sum = x 101
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31. Floating-point Addition
9.999 x x10-1
Step3 : correct it (normalization) :
x 10 1 = x 102
Step4 : Four digits for significand
1.002 x 102
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32. Example Floating-point Addition
0.5 + ( )
0.5 = 1/2 = 1/21 = 0.1 x 20 = 1.00 x 2-1
= -7/16 = -7/24 =
= x 2-2
step 1 : x 2-1
step 2 : 1.0x ( x 2-1)=0.001 x 2-1
step 3 : 1.0 x 2 -4
step 4 :
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33. Multiplication Floating-point
Study in Text Book by yourself.
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34. Next on Lecture 4
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