【计组】定点小数的原码补码乘以或除以2的倍数，是怎么计算的？

一叶箛星墜涳城丶 2014-07-05 10:52:16
比如定点小数X=0.1101 X原=01101 X补=X原=01101
则（2X）原=？ 2* X原=？
（1/2 X）原=？ 1/2 * X原=？
是怎么移位的？

如果定点小数是负数 Y=-0.1101 Y原=11101 Y补=10011
则（2Y）原=？ 2* Y原=？
（1/2 Y）原=？ 1/2 * Y原=？
是怎么移位的？
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赵4老师 2014-07-07
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仅供参考
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
float f;
double d;
void showf() {
    char bs[65];
    char b[65];
    unsigned char *p;
    char e[12];
    char *t;
    int ex;

    printf("\nf=%.6f\n",f);
    p=(unsigned char *)&f;
    printf("hex=%02X %02X %02X %02X\n",p[3],p[2],p[1],p[0]);
    ltoa(*(long *)&f,b,2);
    sprintf(bs,"%032s",b);
    printf("bin=%s\n",bs);
    printf("bin=%.1s %.8s   %s\n",bs,bs+1,bs+9);
    strncpy(e,bs+1,8);e[8]=0;
    ex=strtol(e,&t,2);
    printf("    %c %-4d-127 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+9);
    ex-=127;
    printf("    %c %-8d 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+9);
}
void showd() {
    char bs[65];
    char b[65];
    unsigned char *p;
    char e[12];
    char *t;
    int ex;

    printf("\nd=%.15lf\n",d);
    p=(unsigned char *)&d;
    printf("hex=%02X %02X %02X %02X %02X %02X %02X %02X\n",p[7],p[6],p[5],p[4],p[3],p[2],p[1],p[0]);
    _i64toa(*(__int64 *)&d,b,2);
    sprintf(bs,"%064s",b);
    printf("bin=%s\n",bs);
    printf("bin=%.1s %.11s   %s\n",bs,bs+1,bs+12);
    strncpy(e,bs+1,11);e[11]=0;
    ex=strtol(e,&t,2);
    printf("    %c %-6d-1023 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+12);
    ex-=1023;
    printf("    %c %-11d 1.%s\n",(bs[0]=='0')?'+':'-',ex,bs+12);
}
int main() {

    for (f=0.0f;f<=2.2f;f+=0.2f) showf();
    printf("------------\n");
    f=2.0f;showf();
    printf("-----------------------------------\n");
    for (d=0.0 ;d<=2.2 ;d+=0.2 ) showd();
    printf("------------\n");
    d=2.0 ;showd();

    return 0;
}
//
//f=0.000000
//hex=00 00 00 00
//bin=00000000000000000000000000000000
//bin=0 00000000   00000000000000000000000
//  + 0   -127 1.00000000000000000000000
//  + -127     1.00000000000000000000000
//
//f=0.200000
//hex=3E 4C CC CD
//bin=00111110010011001100110011001101
//bin=0 01111100   10011001100110011001101
//  + 124 -127 1.10011001100110011001101
//  + -3       1.10011001100110011001101
//
//f=0.400000
//hex=3E CC CC CD
//bin=00111110110011001100110011001101
//bin=0 01111101   10011001100110011001101
//  + 125 -127 1.10011001100110011001101
//  + -2       1.10011001100110011001101
//
//f=0.600000
//hex=3F 19 99 9A
//bin=00111111000110011001100110011010
//bin=0 01111110   00110011001100110011010
//  + 126 -127 1.00110011001100110011010
//  + -1       1.00110011001100110011010
//
//f=0.800000
//hex=3F 4C CC CD
//bin=00111111010011001100110011001101
//bin=0 01111110   10011001100110011001101
//  + 126 -127 1.10011001100110011001101
//  + -1       1.10011001100110011001101
//
//f=1.000000
//hex=3F 80 00 00
//bin=00111111100000000000000000000000
//bin=0 01111111   00000000000000000000000
//  + 127 -127 1.00000000000000000000000
//  + 0        1.00000000000000000000000
//
//f=1.200000
//hex=3F 99 99 9A
//bin=00111111100110011001100110011010
//bin=0 01111111   00110011001100110011010
//  + 127 -127 1.00110011001100110011010
//  + 0        1.00110011001100110011010
//
//f=1.400000
//hex=3F B3 33 34
//bin=00111111101100110011001100110100
//bin=0 01111111   01100110011001100110100
//  + 127 -127 1.01100110011001100110100
//  + 0        1.01100110011001100110100
//
//f=1.600000
//hex=3F CC CC CE
//bin=00111111110011001100110011001110
//bin=0 01111111   10011001100110011001110
//  + 127 -127 1.10011001100110011001110
//  + 0        1.10011001100110011001110
//
//f=1.800000
//hex=3F E6 66 68
//bin=00111111111001100110011001101000
//bin=0 01111111   11001100110011001101000
//  + 127 -127 1.11001100110011001101000
//  + 0        1.11001100110011001101000
//
//f=2.000000
//hex=40 00 00 01
//bin=01000000000000000000000000000001
//bin=0 10000000   00000000000000000000001
//  + 128 -127 1.00000000000000000000001
//  + 1        1.00000000000000000000001
//------------
//
//f=2.000000
//hex=40 00 00 00
//bin=01000000000000000000000000000000
//bin=0 10000000   00000000000000000000000
//  + 128 -127 1.00000000000000000000000
//  + 1        1.00000000000000000000000
//-----------------------------------
//
//d=0.000000000000000
//hex=00 00 00 00 00 00 00 00
//bin=0000000000000000000000000000000000000000000000000000000000000000
//bin=0 00000000000   0000000000000000000000000000000000000000000000000000
//  + 0     -1023 1.0000000000000000000000000000000000000000000000000000
//  + -1023       1.0000000000000000000000000000000000000000000000000000
//
//d=0.200000000000000
//hex=3F C9 99 99 99 99 99 9A
//bin=0011111111001001100110011001100110011001100110011001100110011010
//bin=0 01111111100   1001100110011001100110011001100110011001100110011010
//  + 1020  -1023 1.1001100110011001100110011001100110011001100110011010
//  + -3          1.1001100110011001100110011001100110011001100110011010
//
//d=0.400000000000000
//hex=3F D9 99 99 99 99 99 9A
//bin=0011111111011001100110011001100110011001100110011001100110011010
//bin=0 01111111101   1001100110011001100110011001100110011001100110011010
//  + 1021  -1023 1.1001100110011001100110011001100110011001100110011010
//  + -2          1.1001100110011001100110011001100110011001100110011010
//
//d=0.600000000000000
//hex=3F E3 33 33 33 33 33 34
//bin=0011111111100011001100110011001100110011001100110011001100110100
//bin=0 01111111110   0011001100110011001100110011001100110011001100110100
//  + 1022  -1023 1.0011001100110011001100110011001100110011001100110100
//  + -1          1.0011001100110011001100110011001100110011001100110100
//
//d=0.800000000000000
//hex=3F E9 99 99 99 99 99 9A
//bin=0011111111101001100110011001100110011001100110011001100110011010
//bin=0 01111111110   1001100110011001100110011001100110011001100110011010
//  + 1022  -1023 1.1001100110011001100110011001100110011001100110011010
//  + -1          1.1001100110011001100110011001100110011001100110011010
//
//d=1.000000000000000
//hex=3F F0 00 00 00 00 00 00
//bin=0011111111110000000000000000000000000000000000000000000000000000
//bin=0 01111111111   0000000000000000000000000000000000000000000000000000
//  + 1023  -1023 1.0000000000000000000000000000000000000000000000000000
//  + 0           1.0000000000000000000000000000000000000000000000000000
//
//d=1.200000000000000
//hex=3F F3 33 33 33 33 33 33
//bin=0011111111110011001100110011001100110011001100110011001100110011
//bin=0 01111111111   0011001100110011001100110011001100110011001100110011
//  + 1023  -1023 1.0011001100110011001100110011001100110011001100110011
//  + 0           1.0011001100110011001100110011001100110011001100110011
//
//d=1.400000000000000
//hex=3F F6 66 66 66 66 66 66
//bin=0011111111110110011001100110011001100110011001100110011001100110
//bin=0 01111111111   0110011001100110011001100110011001100110011001100110
//  + 1023  -1023 1.0110011001100110011001100110011001100110011001100110
//  + 0           1.0110011001100110011001100110011001100110011001100110
//
//d=1.600000000000000
//hex=3F F9 99 99 99 99 99 99
//bin=0011111111111001100110011001100110011001100110011001100110011001
//bin=0 01111111111   1001100110011001100110011001100110011001100110011001
//  + 1023  -1023 1.1001100110011001100110011001100110011001100110011001
//  + 0           1.1001100110011001100110011001100110011001100110011001
//
//d=1.800000000000000
//hex=3F FC CC CC CC CC CC CC
//bin=0011111111111100110011001100110011001100110011001100110011001100
//bin=0 01111111111   1100110011001100110011001100110011001100110011001100
//  + 1023  -1023 1.1100110011001100110011001100110011001100110011001100
//  + 0           1.1100110011001100110011001100110011001100110011001100
//
//d=2.000000000000000
//hex=3F FF FF FF FF FF FF FF
//bin=0011111111111111111111111111111111111111111111111111111111111111
//bin=0 01111111111   1111111111111111111111111111111111111111111111111111
//  + 1023  -1023 1.1111111111111111111111111111111111111111111111111111
//  + 0           1.1111111111111111111111111111111111111111111111111111
//
//d=2.200000000000000
//hex=40 01 99 99 99 99 99 99
//bin=0100000000000001100110011001100110011001100110011001100110011001
//bin=0 10000000000   0001100110011001100110011001100110011001100110011001
//  + 1024  -1023 1.0001100110011001100110011001100110011001100110011001
//  + 1           1.0001100110011001100110011001100110011001100110011001
//------------
//
//d=2.000000000000000
//hex=40 00 00 00 00 00 00 00
//bin=0100000000000000000000000000000000000000000000000000000000000000
//bin=0 10000000000   0000000000000000000000000000000000000000000000000000
//  + 1024  -1023 1.0000000000000000000000000000000000000000000000000000
//  + 1           1.0000000000000000000000000000000000000000000000000000
//
赵4老师 2014-07-07
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引用 4 楼 u010309265 的回复:
虽然我都没看懂 = =
一叶箛星墜涳城丶 2014-07-07
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虽然我都没看懂 = =
一叶箛星墜涳城丶 2014-07-06
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引用 1 楼 u013291805 的回复:
乘2的N次幂就左移N位，除2的N次幂就右移N位。 然后因为是顶点小数，所以他的绝对值必然是小于一的纯小数。 如果只是倍数，那就老老实实的二进制乘除法算呗。
我也知道左移右移。 我写的例题中的答案能写出来不？
Pandorym 2014-07-05
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乘2的N次幂就左移N位，除2的N次幂就右移N位。 然后因为是顶点小数，所以他的绝对值必然是小于一的纯小数。 如果只是倍数，那就老老实实的二进制乘除法算呗。
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