第二章 运算方法和运算器
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Transcript of 第二章 运算方法和运算器
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2.1 --------------------------------------------------------------------------------
2.1.1 2.1.2 2.1.3 2.1.4 2.1.5
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2.1.1 :
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11n +1 2
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012n (0:01):
(012n 01)0||12-n(2.1)
0||2n1 (2.2)
X0 X1X2...Xn
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21N N = RE MM:mantissa)N:(exponent)R: (radix)2816EsMsE1E2EmM1M2Mn
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EsMsE1E2EmM1M2Mn MsE1E2EmM1M2Mn .
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IEEE754 3264: S E M 3231 30 23 22 064S E M 63 62 52 51 0e e 127(01111111) e127.
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32 (1)s(1.)2127e127(2.5)
64 (1)s(1.)21023 e1023 (2.6)
2 00.5
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2 1/2=|M|1 S1=1 S1=0 1 .
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2
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303
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1.2.3.4.
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[1] (41360000)1632
[:]
0100 0001 0011 0110 0000 0000 0000 0000
e127100000100111111100000011=(3)10
1 1.M1.011 0110 0000 0000 0000 0000 1.011011
X(1)s1.M2e (1.011011)23 1011.011(11.375)10
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[2] 20.5937532
[:] 20.5937510100.10011
1210100.100111.01001001124e4
S=0 E4127131M010010011
32 0100 0001 1010 0100 1100 0000 0000 0000(41A4C000)16
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3.
1.()2.
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BCDASCII4 12(c)13(d) 0 123 12 1 2 3 C 0 1 2 D()00
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4.
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BCD
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(1)
(2)
(3)
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2.1.2
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1.01
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X 10 [X] = 1-X=1+|X| 01 X1 = + 0.1011011
X2 = - 0.1011011 [X1]=0.1011011[X2] =1.1011011
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0+0-0[+0]=0.000...0[-0]=1.000...0
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: : 1- 2-n :-(1- 2-n)8168: 127/128-127/12825516: 32767/32768 -32767/32768 65535
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X 2n>X0[X] = 2n-X=2n+|X| 0X>-2nX1 = + 0 1011011
X2 = - 0 1011011 [X1] =01011011[X2] =11011011
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:[+0] =00000000 [-0] =10000000 : 2n-1:-(2n-1) 8168: 127-12725516: 32767 -32767 65535
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2.4 0000~1111 1616= 24 N 2n2
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X 10 [x]= 2+X=2-|X| 0 X-1 X1 = + 0.1011011
X2 = - 0.1011011 [X1]=01011011[X2]=10100101
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X 2n>X0 [x]= 2n+1+X=2n+1-|X| 0X- 2nX1 = + 0 1011011
X2 = - 0 1011011 [X1]=01011011[X2]=10100101
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:n+1: 2n -1 ~ -2n n+1: 1- 2-n ~ - 1 0[0][0]0.0000
0
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[X]=[X] 1X= -01001001 [X]=11001001 [X]=10110110+1=10110111[X]= 28 +X=100000000-1001001= 10110111 10 0 0 0 0 0 0 0 - 1 0 0 1 0 0 1 1 0 1 1 0 1 1 1
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3 1
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:
X 1 X 0[X]= (2- 2-n )+X 0 X > -1
X1=+0.1011011 [X1] =0.1011011X2= -0.1011011 [X2] =1.0100100
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: X 2n > X 0 [X]= (2n+1 -1)+X 0 X > -2n X3=+1011011 [X3] =01011011 X4= -1011011 [X4] =10100100 0: [+0]=00000000 [-0] =11111111
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4.[X]= 2n + X 2n > X -2n X1 = 0101 0101[X1]=0101 0101[X1]=1101 0101X2 = -0101 0101[X2]=1010 1011[X2]=0010 1011
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[X][X] [X] 01 [X]10X[X]=[X] =[X] X0 [X] [X] [X][X]
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[5]16151(1)??(2)??
[:](1)(2151)10(32767)10 0 111 111 111 111 111 (2151)10(32767)10 1 111 111 111 111 111 (2) (1215)10(0.111...11)2 (1215)10(0.111..11)2
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[6]SEM32 (1)s(1.M)2E128 [:](1): 0 11 111 111 111 111 111 111 111 111 111 11 [1(12-23)]2127
(2) : 0 00 000 000 000 000 000 000 000 000 000 00 1.02128
(3): 1 11 111 111 111 111 111 111 111 111 111 11 [1(1223)]2127
(4): 1 00 000 000 000 000 000 000 000 000 000 00 1.02128
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2.1.3 1. ASCII(128 95959533031127
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2.
24
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1.
:
2.1.4
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2.
ASCII0 1
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3.
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2.1.5
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(01n1)n
C01n1 (2.15)
1C1C0
C01n1 (2.16)
1C0
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A B AC(01n1C)BB('0'1'n1C ')
F'0'1'n1C '
F1F0
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[7]5 [:] 801 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 10 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 01 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1
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2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5
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[X]+[Y] = [X+Y] : [X-Y]=[X]+[-Y]
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2.2.1 [][][] (mod 2) :22
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[8] 0.1001 0.0101[:] []0.1001 []0.0101
[]0.1001 []0.0101 []0.1110
0.1110
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[9] 0.1011 0.0101[:][]0.1011[]1.1011
[]0.1011 []1.1011 [] 10.0110
0.0110
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2.2.2
[][][][][] [][][]1[]
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[10] 10.111020.1101[1][1][2][2]
[:][1]1.0010[1]0.1110[2]0.1101[2]1.0011
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[11] 0.11010.0110[:][]0.1101[]0.0110[]1.1010 [] 0.1101 [] 1.1010 [] 10.0111
0.0111
- 2.3 ||
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[12] 0.1011 0.1001
[:]
[]0.1011 []0.1001
[]0.1011 []0.1001 []1.0100
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[13] 0.1101 0.1011
[:]
[]1.0011 []1.0101 []1.0011 []1.0101 []0.1000
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:
::
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42
1.
2. 4
. Sf1Sf2
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[14] 0.1100 0.1000
[:]
[]00.1100[]00.1000
[]00.1100 []00.1000 01.0100
011
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[15] 0.1100 -0.1000
[:] []11.0100[]11.1000
[]11.0100 []11.1000 10.1100
101
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1. 4 VSf1Sf2Sf1Sf2
2. 4
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00011011 OVR = Sf1 Sf2 = 1 OVR = Sf1 Sf2 = 0
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12VCfCoCfCo
. SC
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CS [X]= 1. 1 0 1 [X]= 1. 1 1 0 + [Y]= 1. 00 1 + [Y]= 0.1 0 0 [X+Y]= 10.1 1 0 [X+Y]= 10.0 1 0 C=0S=1 C=1S=1 X+Y=+0.010
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2.2.4 / AiBiCiSiCi1 2.2 2.2 SiAiBiCi Ci1AiBiBiCiCiAi (2.23)
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2.2
Ai
Bi
Ci
Si
Ci+1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
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n1(FA)nM
M0(AB)M1(AB)AB[A][B]B1MM11
CnCn1CnCn1
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(FA)Si6T(3T)Ci15TTT
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n2.2(a)nta
tan2T9T(2n9)T (2.22)
9T2T
ta(n-1)2T9T
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2.2.5 BCD()
nBCDn4BCDBCD
- iiCi
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2.3.1 1. :2.3
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n() []f .n110 []f .n110[](ff)(0.n110)(0.n110) ff ()
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0.11010.1011.:
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:100
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nn2n n 1
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2. :ABC 1 2.NN
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3AC
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:X=0.1101Y=0.1011XY. B=X Cd=4. :1()
1()
0()
1()XY=0.10001111
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A.B110CdnSxSy
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1. R0Z0R2XR1YR1R0 2.
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R0 R1 ynALU R2CxQQynynRSLDR0LDR1T1T2+1Ti
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3.
Aam1a1a0
Bbn1b1b0
ab
m1n1 a ai2ib bj2j i0j0
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ABmnP
Ppmn1p1p0
P
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mn()aibj
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mn{aibj|0im10jn1}mn12.4 mn
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55[16]A 11011B 10101aibjp9p8p0
[:] a4b01 a3b01 a2b00 a1b01 a0b01a4b10 a3b10 a2b10 a1b10 a0b10a4b21 a3b21 a2b20 a1b21 a0b20a4b30 a3b30 a2b30 a1b30 a0b30a4b41 a3b41 a2b40 a1b41 a0b41
Pp9p8p7p6p5p4p3p2p1p01000110111 (56710)
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4.(1) 2
2
C10 CiaiCi1
ai*aiECi10in
2
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(2) (n1)(n1)
AB()
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A=anan-1a1a0B=bnbn-1b1b0(n1)ABnn2n:ABPp2n1p1p0p2nanbnP2n 1
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[17] 1513
[:] [] 01111 [] 11101 ||1111||11011111000011 ( 11000011)2=(-195)10 15 (13) 195
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2.4 2.4.1
n()[]f .n110[]f .n110 q/[q](ff)+(0.n110/0.n110)
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0.10010.1011: 0.1 1 0 1q0.1 0 1 1 0.1 0 0 1 0 (r0)00.0 1 0 1 1 2111 0.0 0 1 1 1 0 r1 r10.0 0 1 0 1 1 22110.0 0 0 0 1 1 0 r2r20.0 0 0 1 0 1 1 23100.0 0 0 0 1 1 0 0 r3 r30.0 0 0 0 1 0 1 1 24110.0 0 0 0 0 0 0 1 r4r4
q0.1101r0.00000001
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1. 211r021r1 3. r122r1>221r122r24. r223r22421r324r4
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: : 1
- 1. (1)|X|
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1. R0R2R1 n R1R0 2. 3.R1R0n+1 n+1 n0
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R0 R1 qnALU R2CxQQqnqnRSLDR0LDR1T1T2+1Ti+1ff
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R0R2R1XR0R00-YR0100nn-n
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2.4.2 1./(CAS) /(CAS)P0CASP1CAS
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CASSiAi(BiP)Ci Ci1(AiCi)(BiP)AiCi (2.32)
P0(FA)P1CiCi1
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2.01 440.123456 ()0.1230.q1q2q30.00r3r4r5r6 n14
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/(CAS)(n1)(n1)(n1)2CAS()
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6() 0.123456 3 0.123q3 q0.q1q2q3r6 r0.00r3r4r5r6
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P12CAS
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()CAS3T2nn(n1)2td3(n1)2Tn
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2.5 2.5.1 2.5.2 2.5.3 2.5.4
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2.5.1
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1.
012n012nii(i012n)[21] 1010010112111100001 2[:] 110110100 200001111
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2. V 01n 01n 012n iii(i012n) [22] 1010000110011011 [:] 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 1 10111011
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3. 01n 01n 012n iii(i012n)
[23] 1011100111110011[:]1 0 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 0 1 10110001
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4. 2 01n 01n 012niii(i012n) [24] 1010101111001100[:]1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 01100111
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2.5.2 /(ALU) (FA)/ /(ALU)
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1. (FA) FiAiBiCi Ci1AiBiBiCiCiAi (2.35) AiBiS0S1S2S3XiYiXiYi
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2.10ALU
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/ FiXiYiCni Cni1XiYiYiCniCniXi
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2. S0 S1 S2 S3 Ai Bi YXYiS0 S1AiBiXiS2 S3AiBi2.4(52) 2.4 XiYi52 XiYi XiS2S3S2S3AiBi S2S3 AiBi S2S3 Ai
YiS0S1AiS0S1AiBiS0S1AiBi
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ALU
FiYiXiCn+ iCni1YiXiCni
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42.3601
Cn1Y0X0Cn
Cn012
Cn2Y1X1Cn1Y1Y0X1X0X1Cn
23
Cn3Y2X2Cn2Y2Y1X1Y0X1X2X0X1X2Cn
-
34
Cn4Y3X3Cn3Y3Y2X3Y1X2X3Y0X1X2X3X0X1X2X3Cn
GY3Y2X3Y1X2X3Y0X1X2X3PX0X1X2X3
Cn4GPCn
-
ALUGP
ALU(CLA)
Cn+4()0Cn
4/(ALU)
-
S0S3ALU
0F YX C 0
1C 0F Y X 13.
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//
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2.574181ALU:16 1616 1.2.5 2.AB1(1)AB 3.ABALUAB"
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4.ALU 74181ALUPG74181PG74182CLA
474181P0G0G1P1P2G2P3G374182CLA
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CnG0P0Cn
CnG1P1CnG1G0P1P0P1Cn
CnG2P2CnG2G1P2G0P1P2P0P1P2Cn
Cn4 G3P3CnG3G2P3G1P1P2G0P1P2P3P0P1P2P3Cn G*P*Cn
P*P0P1P2P3
G*G3G2P3G1P1P2G0P1P2P3
-
TTL74182G*P*
-
74181ALU74182CLAALU
-
1632ALU74181ALU74182CLA16CLAALU
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2.5.3
CPUCPUI/O
-
2.14(a)4
-
2.14
-
EDE0D1E1E0
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2.5.4 ALU
ALU
-
1. ALU ALUABCPU
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2. ALU ALUALUALU:
-
1.ALU
2.12ALUALU12
-
3.
ALUALU ALU 23ALU
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2.6 2.6.1
2.6.2
2.6.3
2.6.4
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2.6.1
2Ex M
2EM
EEMM
(M2EEM)2EE
-
1. 0 2.
3.
4.
-
(1) 0
00
-
(2)
E EE (1E
-
(3)
-
(4)
01.10.1111.M
-
(5)
01011 1""1"
-
(6) 1
-
[25] 20100.110110112100(0.10101100)
[:][]00 0100.11011011[]00 1001.01010100 EEE[E][E]00 01011 10011 110E2ME2 []00 1000.00110110(11)(11)M2
-
0. 0 0 1 1 0 1 1 0 (11) 1. 0 1 0 1 0 1 0 0 1. 1 0 0 0 1 0 1 0 (11)
1.00010101(10) 00 011
-
011. 0 0 0 1 0 1 0 1 11. 0 0 0 1 0 1 1 0
00
2011(0.11101010)
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2.6.2 1.
2Ex M
2EM 2(EE)(MM)
-
2(E- E)(MM)
-
2.
0
/
/
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(1)
11[]2n2n2n[][]2n2n 2n(2n()) 2n[]1
-
[][]2n1[][]2n2n1 2n1(2n()) [][][](mod 2n1) [][][]
-
0 1 01 0 1 0
-
[26] 011110[] []
[:][]01 011 []00 110 []11 010[][][]10 001 [][][]00 101 3
-
(2)
-
111 0111
-
00 0 10 10 1
-
[27] [1]11.01100000[2]11.01100001[3]11.01101000[4]11.011110014
[:][1]11.0110()
2]11.0110()
[3]11.0110()
[4]11.1000()
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[28] 250.011001123(0.1110010)4()8[]8()[:][M]0.0110011 [M]1.0001110[E]01 011 [E]00 011 [E]00 011[]00 011 0.0110011 [] 01 011 1.0001110(1) [EE][E][E]00 01100 01100 110 2
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(2) [M][M][0.0110011][1.0001110] [1.10100101001010](3) 00 101(-3) 1.01001010010100
(4) 1.0100101 []00 1011.0100101 23(0.1011011)
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2.6.3 1.
- T k T{T1T2Tk} i
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(Si): (Si) ,(L),(C),
Siilmax{i}lml f1/
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k n Tkk(n1) (2.45) kkn1n1nTLnk(2.46)
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TLTkk
TL nkCk Tk k(n1)
n>>k Ck>k kk
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2.
0442.1803
-
X=1.100022 Y=1.110024
XYX=0.011024
111.000125
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[29] 0 170ns 260ns390ns 480nsL tl10ns(1) 4 (2)75ns()[:](1)90ns10ns100ns1234 300ns 4Ck300/1003(2) 75nsCk300/754
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2.6.4 1.CPU
80x87Intel80x86CPU 80x87
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(1)8038680x87386I/O386CPU80x8738638680x8780x8780x8780x8738680x8738680x8780x8738680x8780x87386
-
(2)7IEEE754 80x87 80
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2.CPU
CPU84 (DF)(D1)(D2)(EX)UV41(X1)2(X2)(WF)(ER)U
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88080IEEE754808048610
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2