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Computer Arithmetic (¿µ¹®)

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TZ-SHR-1056032
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2019.09.19
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34 page / 3.60 MB
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Microsoft PowerPoint (pptx)
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  arithmetic & logic unit  roles of alu  does the computations  
everything else in the computer is there to service this unit handles integers
fpu (floating point unit)-arithmetic unit that handles floating point (real) numbers
implementation  
all microprocessors has integer alus on-chip or off-chip fpu (co-processor)
alu inputs and outputs  prentice hall inc.all rights reserved    integer representation  
only have 0 & 1 to represent everything two representative representations
sign-magnitude  two¡¯s compliment  sign-magnitude  left most bit is sign bit 0 means positive  1 means negative  example  xxxx.xx.xx  
-xxxx.xx.xx010
problems  
need to consider both sign and magnitude in arithmetic two representations of zero (0 and-0)
  2¡¯s complement  given n, 2¡¯s complement of n with n bits  
2n-n (2n-1)-n 1 bit complement of n 1 32 bit number
positive numbers : 0 (x 00) to xxx-xxx (x7fffffff) negative numbers :-1 (xffffffff) to-231 (x8 )
like sign-magnitude, msb represents the sign bit
examples  3 011  2 010  1 001  0   
-1 111
-2 110
-3 101
-4 100
  characteristics of 2¡¯s complement  a single representation of zero  
negation is fairly easy (bit complement of n 1)
3 11  boolean complement gives xxxx.xx.xx  add 1 to lsb xxxx.xx.xx  overflow occurs only  
when the sign bit of two numbers are the same but the result has the opposite sign (v cn cn-1)
arithmetic works easily (see later)  
to perform a-b, take the 2¡¯s complement of b and add it to a a (2n-b) a-b 2n (if a > b, ignore the carry)
2n-(b-a) (if b > a, 2¡¯s complement of b-a)
operation  a  b  overflow condition  a b      
-
a b     (ÀÌÇÏ »ý·«)

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