-
- , 5
http://www.cslab.ece.ntua.gr/courses/comparch
[email protected] 2008-2009
-
Decimal E
Hex (4 bits / symbol)
Binary +,-,*,/ ????
[email protected] 2008-2009
-
(radix) r
: m-1m-20, -1-2-n : 0,, -1
..1821,352(10) = 1103 + 8102 + 2101 + 1100 + 310-1 + 510-2 +
210-31256,124(8) = 183 + 282 + 581 + 680 + 18-1 + 28-2 + 48-3
[email protected] 2008-2009
-
[email protected] 2008-2009
-
COMPUTER ARITHMETIC , pointers .
bits (Overflow)1101 + 0101 = 1 0010
[email protected] 2008-2009
-
n bits 2n MSB (Most Significant Bit), LSB (Less Significant
Bit)3 : , 1, 2
[email protected] 2008-2009
-
- To MSB (0 +, 1 -) bits .. 12 bits +1764(10) : 011011100100
-1764(10) : 111011100100 -2n-1+1 2n-1-1To 0 2 (0000 1000)
[email protected] 2008-2009
-
-
, Cn
, Cn
[email protected] 2008-2009
-
-
= =
[email protected] 2008-2009
-
- : : , .. : 0
[email protected] 2008-2009
-
1 To MSB (0+, 1-) n bits.. 12 bits +1764(10) : 011011100100
-1764(10) : 100100011011 -2n-1+1 2n-1-1To 0 2 (0000 1111)
0
[email protected] 2008-2009
-
2To MSB (0+, 1-) n bits .. 12 bits +1764(10) :011011100100
-1764(10) :100100011011 +000000000001 --------------------
100100011100A 2 z, n bits : z + = 2n -2n-1 2n-1-1To 0 1 (0000)
[email protected] 2008-2009
-
2
bit-bit
001100 001100 110100 110100
101110+010001+101111+010001+101111+101110--------------------------------------------------
------------ 011101 1110111000101 1100011 1011100
[email protected] 2008-2009
-
2 /
-
:
[email protected] 2008-2009
-
2
:
[email protected] 2008-2009
-
2 (interrupt / exception) (. C) (. Fortran, Ada)
[email protected] 2008-2009
-
n m, n+m
;
[email protected] 2008-2009
-
[email protected] 2008-2009
-
64 bits
[email protected] 2008-2009
-
[email protected] 2008-2009
-
BOOTH Andrew Booth 1951 2 2 : bits m k 1. 2k+1 2m
: * Multiplier = M * 2k+1 - M * 2m
[email protected] 2008-2009
-
BOOTH :ultiplier = 14 = 001110 k = 3, m = 1 24 - 21 = 16 - 2 =
14 M * Multiplier = M * 24 - M * 21 4 1
[email protected] 2008-2009
-
BOOTH (multiplicand) * Q * (multiplier)
bit :01 : 1 10 : 1 00, 11 :
1 bit ( )
[email protected] 2008-2009
-
BOOTH
[email protected] 2008-2009
-
n bits ( ) ()
2 :
[email protected] 2008-2009
-
n bits : n=1+ n1 + n2MSB n1 bits ( )n2 bits ( )
[email protected] 2008-2009
-
.. 8 bits, 14 bits 0 1111 , 111 = 15,875(10) 1 0000 , 000 =
-15,875(10) 256 [-15,875 15,875] 2-3 = 0,001(2) = 0,125(10) :
2-4
[email protected] 2008-2009
-
: = (-1)sign 2e = (mantissa / significant)e = (exponent)
: 101,011 = 101,011 20 =1,01011 22 = 0,101011 23 = 101011
2-3
(normal form):1,xxxxxxxx 2e
[email protected] 2008-2009
-
: 2-n1-1 2e : 2-n1-1
[email protected] 2008-2009
-
bits bits (floating point overflow) (floating point underflow)
754 floating point standard :Single precision: 8 bits , 23 bits
Double precision : 11 bits , 52 bits bit 1 ( ) 1 bit
[email protected] 2008-2009
-
Min = 00000Max = 111..11 754 = 127 single precision = 1023
double precisionN = (-1)sign (1 + ) 2e-biase = = 0 = 0e = 0, 0 e =
255/2047, = 0 = e = 255/2047, 0 = aN ( )
[email protected] 2008-2009
-
Decimal : - 0.75 = - ( + ) Binary: - 0.11 = - 1.1 x 2-1Floating
point:= 126 = 01111110 = 1
[email protected] 2008-2009
-
(integer arithmetic unit) ???
[email protected] 2008-2009
-
[email protected] 2008-2009
-
[email protected] 2008-2009
