{"id":740,"date":"2009-10-26T16:25:00","date_gmt":"2009-10-26T08:25:00","guid":{"rendered":"http:\/\/note.systw.net\/note\/?p=740"},"modified":"2023-11-04T16:31:26","modified_gmt":"2023-11-04T08:31:26","slug":"%e7%ae%97%e8%a1%93%e9%81%8b%e7%ae%97%e7%9a%84%e6%96%b9%e6%b3%95%e8%88%87%e9%9b%bb%e8%b7%af","status":"publish","type":"post","link":"https:\/\/systw.net\/note\/archives\/740","title":{"rendered":"\u7b97\u8853\u904b\u7b97\u7684\u65b9\u6cd5\u8207\u96fb\u8def"},"content":{"rendered":"\n

\u6574\u6578\u7684\u8868\u793a\u6cd5<\/strong>
\u6574\u6578\u7684\u8868\u793a\u6cd5\u6c7a\u5b9a\u904b\u7b97\u65b9\u6cd5
\u6574\u6578\u7684\u9577\u5ea6\u6c7a\u5b9a\u53ef\u8868\u793a\u7bc4\u570d
\u6574\u6578\u9577\u5ea6=\u7b97\u8853\u908f\u8f2f\u904b\u7b97\u55ae\u5143\u7684\u8cc7\u6599\u9577\u5ea6=word(\u5b57\u7d44)\u7684\u9577\u5ea6<\/p>\n\n\n\n

……………………………………………………………………………………………………….<\/p>\n\n\n\n

complement(\u88dc\u6578\u8868\u793a\u6cd5)
1\u6700\u9069\u5408\u52a0\u6e1b\u6cd5\u904b\u7b97\u7684\u6574\u6578\u8868\u793a\u6cd5
2\u53ef\u8868\u793a\u6b63\u6574\u6578\u8207\u8ca0\u6574\u6578
3\u5927\u591a\u96fb\u5b50\u8a08\u7b97\u6a5f\u63a1\u7528complement\u8868\u793a\u6574\u6578<\/p>\n\n\n\n

\u8a2db\u70ba\u57fa\u5e95\uff0c\u4f7f\u7528n\u500b\u4f4d\u6578\u8868\u793a\u4e00\u6574\u6578\uff0c
\u5247\u6574\u6578x\u7684\u88dc\u6578\u6709\u4ee5\u4e0b\u5169\u7a2e\u8868\u793a\u6cd5:
1\u6574\u6578x\u7684\u88dc\u6578=b^n-x  (b\u7684\u88dc\u6578)
ex:b=10,n=4,\u6574\u6578x=3725
\u5247x\u7684\u88dc\u6578=10^4-3725=6275
\u82e50~4999\u70ba\u6b63,5000~9999\u70ba\u8ca0,\u52476275\u8868\u793a-3725\uff0c\u800c\u4e14\u6574\u6578\u7bc4\u570d\u503c=-5000~4999
\u4e143275+6275=10000=\u6574\u6578\u76840
ex:b=16,n=4,\u6574\u6578x=3562
\u5247x\u7684\u88dc\u6578\uff1d16^4-3562=CA9E
ex:b=8,n=4,\u6574\u6578x=3562
\u5247x\u7684\u88dc\u6578\uff1d8^4-3562=4216
ex:b=2,n=4,\u6574\u6578x=1011
\u5247x\u7684\u88dc\u6578\uff1d2^4-1011=0101
2\u6574\u6578x\u7684\u88dc\u6578=(b^n-1)-x  (b-1\u7684\u88dc\u6578)
ex:b=10,n=4,\u6574\u6578x=3725
\u5247x\u7684\u88dc\u6578=(10^4-1)-3725=6274
\u82e50~4999\u70ba\u6b63,5000~9999\u70ba\u8ca0,\u52476274\u8868\u793a-3725\uff0c\u800c\u4e14\u6574\u6578\u7bc4\u570d\u503c=-4999~4999
\u4e143275+6274=9999=\u6574\u6578\u76840
ex:b=16,n=4,\u6574\u6578x=3562
\u5247x\u7684\u88dc\u6578\uff1d(16^4-1)-3562=CA9D
ex:b=8,n=4,\u6574\u6578x=3562
\u5247x\u7684\u88dc\u6578\uff1d(8^4-1)-3562=4216
ex:b=2,n=4,\u6574\u6578x=1011
\u5247x\u7684\u88dc\u6578\uff1d(2^4-1)-1011=0100<\/p>\n\n\n\n

\u5247\u5be6\u6578x\u7684\u88dc\u6578\u6709\u4ee5\u4e0b\u5169\u7a2e\u8868\u793a\u6cd5:
1 \u5be6\u6578x\u7684\u88dc\u6578=b^n-x  (b\u7684\u88dc\u6578)
ex:b=10,n=2,\u5be6\u6578x=37.25
\u5247x\u7684\u88dc\u6578=10^2-37.25=62.75\uff0c
\u82e50~49.99\u70ba\u6b63,50~99.99\u70ba\u8ca0,\u524762.75\u8868\u793a-37.25\uff0c\u800c\u4e14\u5be6\u6578\u7bc4\u570d\u503c=-50.00~49.99
ex:b=2,n=4,\u5be6\u6578x=1011.101,
\u5247x\u7684\u88dc\u6578\uff1d2^4-1011.101=0100.011
2 \u5be6\u6578x\u7684\u88dc\u6578=(b^n-b^-m)-x  (b-1\u7684\u88dc\u6578)
ex:b=10,n=2,\u5be6\u6578x=37.25,m=2\u4f4d\u5c0f\u6578
\u5247x\u7684\u88dc\u6578=(10^2-10^-2)-37.25=62.74\uff0c
\u82e50~49.99\u70ba\u6b63,50~99.99\u70ba\u8ca0,\u524762.74\u8868\u793a-37.25\uff0c\u800c\u4e14\u5be6\u6578\u7bc4\u570d\u503c=-50.00~49.99
ex:b=2,n=4,\u5be6\u6578x=1011.101,m=3\u4f4d\u5c0f\u6578
\u5247x\u7684\u88dc\u6578\uff1d(2^4-2^-3)-1011.101=0100.010<\/p>\n\n\n\n

……………………………………………………………………………………………………….<\/p>\n\n\n\n

n\u4f4d\u51432\u9032\u4f4d\u6574\u6578\u7684\u8868\u793a\u6cd5
\u7121\u865f\u6578\u8868\u793a\u6cd5<\/strong>
 \u9069\u5408\u52a0\u6cd5\u904b\u7b97\u8207\u6bd4\u8f03\u904b\u7b97
 \u53ea\u80fd\u8868\u793a\u6b63\u6574\u6578\u800c\u7121\u6cd5\u8868\u793a\u8ca0\u6574\u6578
 n\u500b\u4f4d\u5143\u6574\u6578\u503c\u7bc4\u570d=0 ~ 2^n-1
ex:10010110\u5728\u7121\u865f\u6578\u8868\u793a\u6cd5=128+16+4+2=150
\u7b26\u865f\u7d55\u5c0d\u503c\u8868\u793a\u6cd5<\/strong>
 \u5c07\u6700\u5de6\u908a\u7684\u4f4d\u5143\u7576\u6210\u7b26\u865f\u4f4d\u5143\uff0c1\u70ba\u8ca0\u6578\uff0c0\u70ba\u6b63\u6578
 \u9069\u5408\u76f8\u53cd\u6578\u8f49\u63db\uff0c\u4e0d\u9069\u5408\u52a0\u6cd5\u904b\u7b97\u8207\u6bd4\u8f03\u904b\u7b97
 n\u500b\u4f4d\u5143\u6574\u6578\u503c\u7bc4\u570d=-(2^(n-1)-1) ~ (2^(n-1)-1)
ex:10010110\u5728\u7b26\u865f\u7d55\u5c0d\u503c\u8868\u793a\u6cd5=-(16+4+2)=-22
ex:\u7528\u7b26\u865f\u7d55\u5c0d\u503c\u8868\u793a\u6cd5\uff0c69=01000101\uff0c-69\uff1d11000101
1’s complement(<\/strong>1\u7684\u88dc\u6578\u8868\u793a\u6cd5)<\/strong>
 \u9069\u5408\u52a0\u6cd5\u904b\u7b97\u8207\u76f8\u53cd\u6578\u8f49\u63db\uff0c\u4e0d\u9069\u5408\u6bd4\u8f03\u904b\u7b97
 \u4e0d\u9700\u8655\u7406\u9032\u4f4d\u65d7\u6a19
 n\u500b\u4f4d\u5143\u6574\u6578\u503c\u7bc4\u570d=-(2^(n-1)-1) ~ (2^(n-1)-1)
 \u6700\u5de6\u908a\u7b26\u865f\u4f4d\u5143\u82e5\u70ba0\u8868\u793a\u6b63\u6578,1\u8868\u793a\u8ca0\u6578
ex:\u8a2dn=8,\u6574\u6578\u7bc4\u570d=-127~127,\u8ca0\u6574\u6578\u7bc4\u570d=10000000~11111111,\u6b63\u6574\u6578\u7bc4\u570d00000000~01111111
ex:10010110\u57281\u7684\u88dc\u6578\u8868\u793a\u6cd5=-((2^8-1)-150)=11111111-10010110=01101001=-105
ex:10010110\u57281\u7684\u88dc\u6578\u8868\u793a\u6cd5=10010110\u7684\u76f8\u53cd=\u8ca0\u768401101001=-105
ex:\u75281\u7684\u88dc\u6578\u8868\u793a\u6cd5\uff0c69=01000101\uff0c-69\uff1d10111010
2’s complement(2\u7684\u88dc\u6578\u8868\u793a\u6cd5)<\/strong>
 \u9069\u5408\u52a0\u6cd5\u904b\u7b97\u8207\u76f8\u53cd\u6578\u8f49\u63db\uff0c\u4e0d\u9069\u5408\u6bd4\u8f03\u904b\u7b97
 \u9700\u8655\u7406\u9032\u4f4d\u65d7\u6a19
 n\u500b\u4f4d\u5143\u6574\u6578\u503c\u7bc4\u570d=-(2^(n-1)) ~ (2^(n-1)-1)
 \u6700\u5927\u6b63\u6574\u6578\u662f(011111……1)\uff0c\u6700\u5c0f\u8ca0\u6578\u662f(10000……0)
 \u53ef\u76f4\u63a5\u4f7f\u7528binary adder(\u4e8c\u9032\u4f4d\u52a0\u6cd5\u5668)\u4f86\u8868\u793a\u6574\u6578\uff0c\u4e00\u822c\u96fb\u5b50\u8a08\u7b97\u6a5f\u7528
ex:1\u500bbyte\u7684\u53ef\u8868\u793a\u7bc4\u570d\u70ba10000000~01111111=-128~127
ex:10010110\u57282\u7684\u88dc\u6578\u8868\u793a\u6cd5=-((2^8)-150)=-106
ex:10010110\u57282\u7684\u88dc\u6578\u8868\u793a\u6cd5=10010110\u7684\u76f8\u53cd+1=\u8ca0\u768401101001+1=-106
ex:\u75282\u7684\u88dc\u6578\u8868\u793a\u6cd5\uff0c69=01000101\uff0c-69\uff1d10111010+1=10111011
exess(\u8d85\u78bc\u8868\u793a\u6cd5)<\/strong>
 \u9069\u5408\u6bd4\u8f03\u904b\u7b97\uff0c\u4e0d\u9069\u5408\u52a0\u6cd5\u904b\u7b97\u548c\u76f8\u53cd\u6578\u8f49\u63db
 n\u500b\u4f4d\u5143\u6574\u6578\u503c\u7bc4\u570d=-(2^(n-1)) ~ (2^(n-1)-1)
ex:10010110\u5728\u8d85\u78bc\u8868\u793a\u6cd5=(128+16+4+2)-128=22
ex:\u7528\u8d85\u78bc\u8868\u793a\u6cd5\uff0c69=11000101\uff0c-69=00111011=(32+16+8+2+1)-128
ps:1\u7684\u88dc\u6578\u82072\u7684\u88dc\u6578\u8868\u793a\u6cd5\u4e5f\u7a31\u70ba\u6709\u865f\u6578\u8868\u793a\u6cd5
ps:nibble\u8868\u793a4bit\uff0ca word=2bytes=16bit
n=4,\u8868\u793a\u6cd5\u6bd4\u8f03\u8868:<\/p>\n\n\n\n

<\/td>\u7121\u865f\u6578<\/td>\u7b26\u865f\u7d55\u5c0d<\/td>1\u7684\u88dc\u6578<\/td>2\u7684\u88dc\u6578<\/td>\u8d85\u78bc<\/td><\/tr>
0000
0001
0010
0011
0100
0101
0110
0111<\/td>		0<\/strong>
1
2
3
4
5
6
7<\/td>		+0<\/strong>
+1
+2
+3
+4
+5
+6
+7<\/td>		+0<\/strong>
+1
+2
+3
+4
+5
+6
+7<\/td>		+0<\/strong>
+1
+2
+3
+4
+5
+6
+7<\/td>		-8
-7
-6
-5
-4
-3
-2
-1<\/td><\/tr>
1000
1001
1010
1011
1100
1101
1110
1111<\/td>		8
9
10
11
12
13
14
15<\/td>		-0<\/strong>
-1
-2
-3
-4
-5
-6
-7<\/td>		-7
-6
-5
-4
-3
-2
-1
-0<\/strong><\/td>		-8
-7
-6
-5
-4
-3
-2
-1<\/td>		+0<\/strong>
+1
+2
+3
+4
+5
+6
+7<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

……………………………………………………………………………………………………….<\/p>\n\n\n\n

\u6574\u6578\u7684\u52a0\u6e1b\u904b\u7b97<\/p>\n\n\n\n

\u52a0\u6cd5\u904b\u7b97\u6cd5\u5247
\u505a\u6cd5\uff1a\u53ef\u7528n-bit adder(n\u4f4d\u5143\u52a0\u6cd5\u5668)\u9032\u884c\u52a0\u6cd5\u904b\u7b97\u4f86\u7522\u751fn\u7684\u5408
\u82e5\u75281\u7684\u88dc\u6578\u8868\u793a\u6cd5\u8981\u8a2d\u5b9a\u9032\u4f4d\u65d7\u6a19
ex:(5)+(-3)
1\u7684\u88dc\u6578\u8868\u793a\u6cd5=(0101)+(1100)=1(0001)=(0001)+1=(0010)=2
2\u7684\u88dc\u6578\u8868\u793a\u6cd5=(0101)+(1101)=1(0010)=2
\u7522\u751f\u7684\u5408\u82e5\u8d85\u51fa\u7bc4\u570d\u5247\u6703\u51fa\u73fearithmetic overflow(\u7b97\u8853\u6ea2\u4f4d)\u7684\u4e2d\u65b7\u4fe1\u865f
\u5224\u65b7\u662f\u5426\u6709arithmetic overflow\u65b9\u6cd5\uff1a
 \u6709\u865f\u6578
 \u7121\u865f\u6578<\/p>\n\n\n\n

\u6e1b\u6cd5\u904b\u7b97\u6cd5\u5247
\u82e5\u75281\u7684\u88dc\u6578\u8868\u793a\u6cd5\u8981\u8a2d\u5b9a\u9032\u4f4d\u65d7\u6a19
\u6709\u865f\u6578
\u505a\u6cd5\uff1a\u5148\u5c07\u6e1b\u865f\u8f49\u6210\u6e1b\u865f\u7684\u88dc\u6578\uff0c\u5728\u4f7f\u7528n-bit adder\u9032\u884c\u52a0\u6cd5\u904b\u7b97\u4f86\u7522\u751fn\u7684\u5408
ex:\u4f7f\u75281\u7684\u88dc\u6578,\u9700\u8003\u616e\u9032\u4f4d\u65d7\u6a19
(5)-(-3)=(0101)-(1100)=(0101)+(0011)=(1000),overflow
(3)-(6)=(0011)-(0110)=(0011)+(1001)=(1100)=-3
ex:\u4f7f\u75282\u7684\u88dc\u6578
(5)-(-3)=(0101)-(1101)=(0101)+(0011)=(1000),overflow
(3)-(6)=(0011)-(0110)=(0011)+(1010)=(1100)=-3
\u7121\u865f\u6578
\u505a\u6cd5\uff1a\u5148\u628a\u5169\u500b\u7121\u865f\u6578\u8996\u70ba\u6709\u865f\u6578\u7684\u6b63\u6578\uff0c\u4e5f\u5c31\u662f\u6700\u5de6\u908a\u591a\u52a01\u500b\u7b26\u865f\u4f4d\u5143\u4e26\u8a2d\u70ba0\uff0c\u5728\u63a1\u7528\u6709\u865f\u6578\u505a\u6cd5\uff0c\u4e26\u8a2d\u5b9a\u9032\u4f4d\u65d7\u6a19
ex:\u7121\u865f\u6578\u75284bit\u8868\u793a\uff0c\u4f7f\u75282\u7684\u88dc\u6578\u6cd5
(12)-(3)=(1100)-(0011)=12+3\u7684\u88dc\u6578=(1100)+(1101)=(1)(1001)=9
(3)-(12)=(0011)-(1100)=3+12\u7684\u88dc\u6578=(0011)+(0100)=(0)(0111),overflow<\/p>\n\n\n\n

\u52a0\u6e1b\u904b\u7b97\u96fb\u8def
half adder(\u534a\u52a0\u5668<\/strong>)
2\u500b\u8f38\u5165\u8b8a\u6578\uff0c\u88ab\u52a0\u6578x\u8207\u52a0\u6578y
2\u500b\u8f38\u51fa\u8b8a\u6578\uff0ccarry(\u9032\u4f4d)\u8207sum(\u548c)
full adder(\u5168\u52a0\u5668)<\/strong>
3\u500b\u8f38\u5165\u8b8a\u6578\uff0c\u88ab\u52a0\u6578x\u8207\u52a0\u6578y\u548c\u9032\u4f4dc
2\u500b\u8f38\u51fa\u8b8a\u6578\uff0ccarry(\u9032\u4f4d)\u8207sum(\u548c)
parallel adder(\u5e73\u884c\u52a0\u6cd5\u5668)\/ripple adder(\u6f23\u6f2a\u52a0\u6cd5\u5668)<\/strong>
\u4f7f\u7528n\u500b\u5168\u52a0\u5668\u4e32\u9023\u5728\u4e00\u8d77
\u6703\u6709delay propagation(\u5ef6\u9072\u7d2f\u7a4d)\u7684\u554f\u984c
carry look-ahead adder(\u9810\u5148\u9032\u4f4d\u52a0\u6cd5\u5668)<\/strong>
\u7121delay propagation\u7684\u554f\u984c
\u4f7f\u7528carry generate signal(\u9032\u4f4d\u7522\u751f\u8a0a\u865f)\u548ccarry propagate signal(\u9032\u4f4d\u50b3\u905e\u8a0a\u865f)
\u4f4d\u5143\u500b\u6578\u589e\u52a0\u6703\u5c0e\u81f4\u8907\u96dc\u5ea6\u5927\u5927\u589e\u52a0<\/p>\n\n\n\n

……………………………………………………………………………………………………….<\/p>\n\n\n\n

\u6574\u6578\u7684\u4e58\u9664\u904b\u7b97<\/p>\n\n\n\n

\u7121\u865f\u6578\u7684\u4e58\u6cd5\u904b\u7b97\u6cd5\u5247
\u6bd4\u6709\u865f\u6578\u4e58\u6cd5\u904b\u7b97\u7c21\u55ae
\u786c\u9ad4\u7d44\u7e54\uff1an\u4f4d\u5143\u52a0\u6cd5\u5668\u96fb\u8def\uff0cn\u4f4d\u5143\u66ab\u5b58\u5668*3\uff0c\u9032\u4f4d\u65d7\u6a19\uff0c\u63a7\u5236\u96fb\u8def<\/p>\n\n\n\n

\u7121\u865f\u6578\u7684\u9664\u6cd5\u904b\u7b97\u6cd5\u5247
\u786c\u9ad4\u7d44\u7e54\uff1an\u4f4d\u5143\u52a0\u6cd5\u5668\u96fb\u8def\uff0cn\u4f4d\u5143\u66ab\u5b58\u5668*3\uff0c\u7b26\u865f\u65d7\u6a19\uff0c\u63a7\u5236\u96fb\u8def
\u904b\u7b97\u6b65\u9a5f
  restoring division(\u6062\u5fa9\u5f0f\u9664\u6cd5)
  non-restoring division(\u975e\u6062\u5fa9\u5f0f\u9664\u6cd5)\uff1a\u6548\u80fd\u8f03\u597d<\/p>\n\n\n\n

\u6709\u865f\u6578\u7684\u4e58\u6cd5\u904b\u7b97\u6cd5\u5247
\u56e0\u70ba\u6709\u7b26\u865f\u4f4d\u5143\u6240\u4ee5\u8981\u505asign extension(\u7b26\u865f\u64f4\u5145)
\u786c\u9ad4\u7d44\u7e54\uff1a
robertson algorithm(<\/strong>\u7f85\u52c3\u68ee\u904b\u7b97\u6cd5\u5247)
 \u76f4\u63a5\u5c0d\u6709\u865f\u6578\u9032\u884c\u4e58\u6cd5\u904b\u7b97\uff0c\u4e0d\u9700\u5c07\u8ca0\u7684\u4e58\u6578\u8f49\u63db\u6210\u6b63\u7684\u4e58\u6578
booth algorithm(<\/strong>\u5e03\u6c0f\u904b\u7b97\u6cd5\u5247)
 \u5c0d\u4e58\u6578\u9032\u884cskipping over 1s(\u8df3\u904e\u9023\u7e8c\u76841)\u7684\u6280\u5de7\u7de8\u78bc
 \u8655\u7406\u6b63\u8ca0\u4e58\u6578\u7684\u65b9\u5f0f\u90fd\u4e00\u6a23
 \u4ee5\u52a0\u6cd5\u6216\u6e1b\u6cd5\u9032\u884c\u904b\u7b97
 \u82e5\u6709\u9023\u7e8c\u76840\u62161\u7684\u4e58\u6578\uff0c\u5247\u6703\u6709\u8f03\u5c11\u904b\u7b97\uff0c\u56e0\u6b64\u53ef\u52a0\u901f\u5b8c\u6210\u4e58\u6cd5
 \u5e73\u5747\u6548\u7387\u81f3\u5c11\u8207\u4e00\u822c\u6709\u865f\u6578\u4e58\u6cd5\u904b\u7b97\u6cd5\u5247\u76f8\u540c
 \u6b65\u9a5f\uff1a
1\u5c07\u4e58\u6578\u7531\u53f3\u800c\u5de6\uff0c\u4e26\u5c0d2\u548c3\u8655\u7406n\u6b21
2\u4e58\u6578\u82e5\u76f8\u9130\u5169\u500b\u4f4d\u5143\u662f01\uff0c\u5247\u5c07\u88ab\u4e58\u6578\u52a0\u5165\u4e58\u7a4d\u4e4b\u4e2d
\u82e5\u76f8\u9130\u5169\u4f4d\u5143\u662f10\uff0c\u5247\u5c07\u88ab\u4e58\u6578\u53d62’s\u88dc\u6578\u518d\u52a0\u5165\u4e58\u7a4d\u4e4b\u4e2d
\u5176\u9918\u968e\u4e0d\u904b\u7b97
3\u5c07\u4e58\u7a4d\u90e8\u4efd\u5f80\u53f3\u79fb\u4e00\u4f4d
bit-pair recoding method<\/strong>(\u4f4d\u5143\u5c0d\u7de8\u78bc\u65b9\u5f0f)
  \u8655\u7406\u6b63\u8ca0\u4e58\u6578\u7684\u65b9\u5f0f\u90fd\u4e00\u6a23
  \u81f3\u591a\u9700\u8981n\/2\u6b21\u7684\u52a0\u6cd5\u904b\u7b97<\/p>\n\n\n\n

\u4e58\u6cd5\u96fb\u8def\u786c\u9ad4\u5be6\u4f5c
\u5fae\u7a0b\u5f0f\u63a7\u5236
  \u7522\u751f\u4e00\u9023\u4e32\u7684\u52a0\u6e1b\u6cd5\u904b\u7b97\u53cashift(\u79fb\u4f4d\u904b\u7b97)\u7684\u63a7\u5236\u4fe1\u865f\u5408\u529b\u5b8c\u6210
  \u96fb\u8def\u7c21\u55ae\uff0c\u4f46\u904b\u7b97\u8981\u6975\u591a\u8a08\u6642\u9031\u671f
\u786c\u9ad4\u7dda\u8def\u63a7\u5236
  \u9ad8\u6548\u80fd\u96fb\u7b97\u6a5f\u7528\uff0c\u6548\u80fd\u4f73<\/p>\n\n\n\n

………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………….<\/p>\n\n\n\n

\u5be6\u6578\u7684\u8868\u793a\u6cd5<\/strong>
fixed-point number(\u5b9a\u9ede\u6578\u8868\u793a\u6cd5)\uff1a\u5c0f\u6578\u9ede\u662f\u56fa\u5b9a\u7684\uff0c\u53ef\u8868\u793a\u7bc4\u570d\u6709\u9650
floating-point number(\u6d6e\u9ede\u6578\u8868\u793a\u6cd5)\uff1a\u5c0f\u6578\u9ede\u662f\u6d6e\u52d5\u7684<\/p>\n\n\n\n

floating-point number
1 \u6d6e\u9ede\u6578\u6b04\u4f4d\uff1a[sign bit][exponent][mantissa]
 sign bit(\u7b26\u865f\u4f4d\u5143)\uff1a\u6d6e\u9ede\u6578\u7528\u7b26\u865f\u7d55\u5c0d\u503c\u8868\u793a\u6cd5\uff0c\u56e0\u6b64\u6700\u5de6\u908a\u7684\u4f4d\u51431\u8868\u8ca0\u65780\u8868\u6b63\u6578
 mantissa(\u5047\u6578)\/fraction(\u5c0f\u6578)\uff1a\u8868\u793asignificant digit\u6709\u6548\u6578\u5b57\u6216precision\u7cbe\u78ba\u5ea6\uff0c\u6700\u5de6\u908a\u9700\u70ba\u975e\u96f6\u7684\u6b63\u898f\u5316\u683c\u5f0f
 exponent(\u6307\u6578)\uff1a\u8868\u793a\u6d6e\u9ede\u6578\u7684\u53ef\u8868\u793a\u7bc4\u570d\uff0c\u4f7f\u7528\u8d85\u78bc\u8868\u793a\u6cd5\uff0c\u56e0\u70ba\u8f03\u9069\u5408\u6bd4\u8f03\u904b\u7b97
   ex:\u82e5\u9577\u5ea6\u70ba8bit,\u57fa\u5e95\u70ba2,\u5247\u7bc4\u570d\u662f2^-128 ~ 2^127
ps:\u6b63\u898f\u5316\u904e\u7a0b\u5c31\u662f\uff0c\u5c07\u5c0f\u6578\u9ede\u5f80\u5de6\u79fb\u6216\u5f80\u53f3\u79fb\u5230\u5c0f\u6578\u9ede\u53f3\u908a\u7b2c\u4e00\u500b\u6578\u5b57\u4e0d\u53ef\u70ba\u96f6
  ex:0.00011\u5c31\u8981\u5c0f\u6578\u9ede\u53f3\u79fb3\u4f4d\u8b8a\u62100.11
  ex:110001.11\u5c31\u8981\u5c0f\u6578\u9ede\u5de6\u79fb6\u4f4d\u8b8a\u62100.11000111
2 \u7528\u5c0f\u6578\u90e8\u4efd\u8207\u6307\u6578\u90e8\u4efd\u8868\u793a\u5be6\u6578
3 \u5be6\u6578\u7684\u503c= (1-2*s)*(0.m)*2^(e-n)
ex:\u8a2d\u6307\u6578\u6b04\u4f4d5bit,\u5047\u657810bit,\u63a1\u4e8c\u9032\u5236\u6b63\u898f\u5316,\u5247\u6d6e\u9ede\u6578
+49.75=+(110001.11)*2^0=+(0.11000111)*2^6<\/strong>=(1-2*0<\/strong>)*(0.11000111)*2^(22<\/strong>-16)=[\u6b63][22][11000111\u586b0\u5230\u6eff]=[0][10110][11000111<\/strong>00]
-356.875=-(101100100.111)*2^0=-(0.101100100111)*2^9<\/strong>=(1-2*1<\/strong>)*(0.101100100111)*2^(25<\/strong>-16)=[\u8ca0][25][\u53ea\u53d61011001001<\/strong>11\u524d10\u500b]=[1][11001][1011001001]
-0.09375=-(0.00011)*2^0=-(0.11)*2^-3<\/strong>=(1-2*1<\/strong>)*(0.11)*2^(13<\/strong>-16)=[\u8ca0][13][11\u586b0\u5230\u6eff]=[1][01101][11<\/strong>00000000]
ps:5bit,\u63a1\u8d8516\u78bc\u8868\u793a\u6cd5,\u7bc4\u570d\u5728-16 ~ 15
ex:\u8a2d\u6d6e\u9ede\u6578\u683c\u5f0f\u70ba[1bit][3bit][4bit],\u5247
01101000=[0][110][1000]=+(0.10<\/strong>00)*2^2<\/strong>=(10.00)=2
100000010=[1][000][0010]=-(0.0010)*2^-4<\/strong>=(0.00000010<\/strong>)=-1\/128<\/p>\n\n\n\n

………………….<\/p>\n\n\n\n

IEEE754\u6d6e\u9ede\u6578\u8868\u793a\u6cd5
1 \u63a1\u75282\u9032\u4f4d\u6b63\u898f\u5316\u4e14\u5c0f\u6578\u9ede\u6700\u5de6\u908a\u96b1\u542b\u4e00\u500b1,\u4f7f\u7528rounding\u8655\u7406guard bit
2 \u82e5\u5c07\u6307\u6578\u6b04\u4f4d\u6240\u6709\u4f4d\u5143\u8a2d\u70ba0\uff0c\u8868\u793aunderflow\u6b20\u4f4d\uff0c\u4e5f\u5c31\u8868\u793a\u5be6\u6578\u503c\u592a\u5c0f\u7121\u6cd5\u8868\u793a
3 \u82e5\u5c07\u6307\u6578\u6b04\u4f4d\u6240\u6709\u4f4d\u5143\u8a2d\u70ba1\uff0c\u8868\u793aoverflow\u6ea2\u4f4d\uff0c\u4e5f\u5c31\u8868\u793a\u5be6\u6578\u503c\u592a\u5927\u7121\u6cd5\u8868\u793a
\u6709\u5169\u7a2e\u683c\u5f0f\uff0c\u5982\u4e0b\uff1a
single precision<\/strong>\u55ae\u500d\u7cbe\u5bc6\u5ea6:32\u4f4d\u5143 [sign(1)][exponent(8)][fractional mantissa(23)]
\u5be6\u6578\u7684\u503c= (1-2*s)*(1.f)*2^(e-127)
ex:-129.625=-(10000001.101)*2^0=-(1.0000001101)*2^7<\/strong>=(1-2*1)*(1.0000001101)*2^(134<\/strong>-127)
=[\u8ca0][134][0000001101\u5f8c\u63a50\u4e00\u76f4\u5230\u6b04\u4f4d\u6eff]=[1][10000110][0000001101<\/strong>000000000000]
ps:134=127+7
ex:-1.5=-(1.1)*2^0=(1-2*1)*(1.1)*2^(127<\/strong>-127)
=[\u8ca0][127][1\u5f8c\u63a50\u4e00\u76f4\u5230\u6b04\u4f4d\u6eff]=[1][01111111][1<\/strong>000000000000000000000]
double precision<\/strong>\u96d9\u500d\u7cbe\u5bc6\u5ea6:64\u4f4d\u5143 [sign(1)][exponent(11)][fractional mantissa(52)]
\u5be6\u6578\u7684\u503c= (1-2*s)*(1.f)*2^(e-1023)<\/p>\n\n\n\n

ps:\u6d6e\u9ede\u6578\u7684\u8aa4\u5dee\u6709
round off error\u62fe\u53bb\u8aa4\u5dee\uff1a\u5132\u5b58\u5047\u6578\u90e8\u4efd\u7684\u9577\u5ea6\u6709\u9650\u800c\u7121\u6cd5\u5b8c\u5168\u5132\u5b58\u800c\u9020\u6210\u7684\u8aa4\u5dee
truncation error\u622a\u5c3e\u8aa4\u5dee\uff1a\u7121\u6cd5\u771f\u6b63\u9032\u884c\u7121\u7aae\u591a\u500b\u904b\u7b97\u800c\u9020\u6210\u7684\u8aa4\u5dee
ps:guard bit
\u8aaa\u660e\uff1a\u5728\u6d6e\u9ede\u904b\u7b97\u904e\u7a0b\u4e2d\uff0c\u8d85\u904e\u5047\u6578\u6b04\u4f4d\u9577\u5ea6\u7684\u90e8\u4efd
\u6700\u5f8c\u8868\u793a\u7d50\u679c\u6642\uff0c\u8655\u7406\u9019\u4e9b\u4f4d\u5143\u4ee5\u7522\u751f\u9577\u5ea6\u8f03\u77ed\u7684\u9032\u4f3c\u503c\u65b9\u6cd5\u6709\uff1a
chopping\u5207\u65b7\uff1a\u76f4\u63a5\u628aguard bit\u6368\u68c4\uff0c\u5176\u9918\u4f4d\u5143\u5b8c\u5168\u4e0d\u8b8a\uff0c\u8aa4\u5dee\uff1a0 ~ 1
von neumann rounding\u8303\u8afe\u66fc\u6368\u53bb\uff1a\u628aguard bit\u53bb\u9664\uff0c\u82e5\u5176\u4e2d\u4e00\u500b\u4f4d\u5143\u70ba1\uff0c\u5247\u628a\u5047\u6578\u4f4d\u5143\u6700\u53f3\u908a\u8a2d\u70ba1\uff0c\u8aa4\u5dee\uff1a+1 ~ -1
rounding\u6368\u53bb\uff1a\u628aguard bit\u53bb\u9664\uff0c\u82e5guard bit\u6700\u5de6\u908a\u4f4d\u5143\u70ba1\uff0c\u5247\u628a\u5047\u6578\u6b04\u4f4d\u6700\u53f3\u908a\u4f4d\u5143\u8a2d\u70ba1\uff0c\u8aa4\u5dee\uff1a+1\/2 ~ -1\/2<\/p>\n\n\n\n

……………………………………………………………………………………………………….<\/p>\n\n\n\n

\u5be6\u6578\u7684\u52a0\u6e1b\u904b\u7b97\u8207\u96fb\u8def
\u6307\u6578\u6b04\u4f4d\u7684\u503c\u9700\u76f8\u540c\u624d\u53ef\u958b\u59cb\u52a0\u6e1b\u6cd5\u904b\u7b97\uff0c\u6b65\u9a5f\u70ba\uff1a
1\u6bd4\u8f03\u6307\u6578\u5927\u5c0f\uff1a\u82e5\u662f\u5169\u6d6e\u9ede\u6578\u7684\u6307\u6578\u76f8\u5deen\uff0c\u5247\u5c07\u6307\u6578\u8f03\u5c0f\u8005\u7684\u5047\u6578\u53f3\u79fbn\u500b\u4f4d\u5143
2\u8a2d\u5b9a\u6307\u6578\uff1a\u5c07\u6700\u5c0f\u8005\u7684\u6307\u6578\u6b04\u4f4d\u8a2d\u6210\u548c\u6700\u5927\u8005\u7684\u6307\u6578\u6b04\u4f4d\u4e00\u6a23
3\u5047\u6578\u76f8\u52a0(\u6e1b) \uff1a\u5c0d\u539f\u5148\u5169\u500b\u6d6e\u9ede\u6578\u4e2d\u7684\u5047\u6578\u90e8\u4efd\u9032\u884c\u52a0(\u6e1b)\u6cd5
4\u6b63\u898f\u5316\uff1a\u5982\u679c\u5047\u6578\u4e0d\u7b26\u5408\u6b63\u898f\u5316\u683c\u5f0f\uff0c\u5c31\u9700\u8981\u5728\u505a\u4e00\u6b21\u6b63\u898f\u5316
ex:[0][11011][1001110100]+[1][01101][1100000000]
1 \u6307\u6578\u6b04\u4f4d[01101]\u6bd4[11011]\u5c0f14bit\uff0c\u6240\u4ee5\u5c07\u6700\u5c0f\u8005\u7684\u5047\u6578\u53f3\u79fb14\u500b\u4f4d\u5143\uff0c\u4e26\u5c07\u6307\u6578\u8a2d\u70ba11011
2 [1][01101][1100000000]\u7684\u8a2d\u5b9a\u5f8c\u8b8a\u70ba[1][11011][0000000000]
3 [0][11011][1001110100]+[1][11011][0000000000]=[1][11011][1001110100]
4 [1][11011][1001110100]\u5df1\u7b26\u5408\u6b63\u898f\u5316\u8981\u6c42
ps:\u5982\u679c\u5169\u9ede\u6d6e\u9ede\u6578\u6307\u6578\u76f8\u5dee\u5927\uff0c\u5247\u6307\u6578\u5c0f\u7684\u6d6e\u9ede\u6578\u5fc5\u9808\u5148\u5c07\u5047\u6578\u6b04\u4f4d\u53f3\u79fb\uff0c\u82e5\u6709\u6548\u6578\u5b57\u8d85\u51fa\u5047\u6578\u6b04\u4f4d\u5247\u6703\u5f62\u6210\u8aa4\u5dee
ex:\u6b04\u4f4d\u683c\u5f0f\u70ba[1bit][3bit][4bit],5\/2+1\/8=5\/2,\u56e0\u70ba
[0][110][1010]+[0][010][1000]=[0][110][1010]+[0][110<\/strong>][0000<\/strong>]=[0][110][1010]=5\/2<\/p>\n\n\n\n

\u9069\u5408\u7ba1\u7dda\u4f5c\u696d\u6210\u70baarithmetic pipeline(\u7b97\u8853\u5c0e\u7ba1)\uff0c\u5728\u8655\u7406\u5927\u91cf\u6d6e\u9ede\u6578\u76f8\u52a0\u904b\u7b97\u6642\u53ef\u5927\u5927\u63d0\u6607\u904b\u7b97\u6548\u7387
ps:arithmetic pipeline\u53ea\u9700\u8655\u7406data hazard(\u8cc7\u6599\u5371\u6a5f)
\u56db\u968e\u6bb5\u5c0e\u7ba1\u8a2d\u8a08\u7684\u6d6e\u9ede\u6578\u52a0\u6cd5\u5668\uff1a
 stage1 \u52a0\u6cd5\u5668(\u6bd4\u8f03\u6307\u6578) 
 stage2 \u79fb\u4f4d\u5668\u8207\u591a\u5de5\u5668(\u5047\u6578\u53f3\u79fb\u8207\u8a2d\u5b9a\u6307\u6578)
 stage3 \u52a0\u6cd5\u5668(\u5047\u6578\u76f8\u52a0)
 stage4 \u52a0\u6cd5\u5668\u8207\u79fb\u4f4d\u5668(\u6b63\u898f\u5316)<\/p>\n\n\n\n

……………………………………………………………………………………………………….<\/p>\n\n\n\n

\u5be6\u6578\u7684\u4e58\u9664\u904b\u7b97\u8207\u96fb\u8def
\u4e58\u9664\u904b\u7b97\u6b65\u9a5f\uff1a
1\u6307\u6578\u76f8\u52a0\uff1a\u5f97\u5230\u7684\u7d50\u679c\u5fc5\u9808\u7528\u8d85\u78bc\u8868\u793a\u6cd5\u8868\u793a\uff0c\u5728\u8f49\u6210\u4e8c\u9032\u4f4d
2\u5047\u6578\u76f8\u4e58\uff1a\u5f97\u5230\u7684\u7d50\u679c\u8d85\u904e\u6b04\u4f4d\uff0c\u5247\u53ea\u4fdd\u7559\u524d\u9762\u7559\u5728\u6b04\u4f4d\u7684\u90e8\u4efd
3\u6b63\u898f\u5316\uff1a\u5982\u679c\u5047\u6578\u4e0d\u7b26\u5408\u6b63\u898f\u5316\u683c\u5f0f\uff0c\u5c31\u9700\u8981\u5728\u505a\u4e00\u6b21\u6b63\u898f\u5316
ex:[0][10100][1001100000]*[1][10010][1111000000]
1\u6307\u6578\u6b04\u4f4d[10100]+[10010]=100110,\u5728\u8d85\u78bc\u8868\u793a\u6cd5\u88e1\u8868\u793a22(\u56e0\u70ba38-16),\u6240\u4ee5\u5f97\u5230[10110]
2\u5047\u6578\u6b04\u4f4d[1001100000]*[1111000000]=[1000111010]
3\u5f97\u5230[1][10110][1000111010]\uff0c\u5df1\u7b26\u5408\u6b63\u898f\u5316<\/p>\n","protected":false},"excerpt":{"rendered":"

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