float浮点数精度

为什么float可以表示的最小数字是2的负二十三次方，精度却只有7位

仅供参考：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
int main() {
    float f;
    double d;
    char bs[65];
    char b[65];
    char s[80];
    unsigned char *p;
    char e[12];
    char *t;
    int ex;
    int flag;

    flag=0;
    while (1) {
        printf("Input a float point number or 0xXXXXXXXX or 0xXXXXXXXXXXXXXXXX:");fflush(stdout);
        rewind(stdin);
        fgets(s,80,stdin);
        if ('\n'==s[0]) return 1;
        if (1==sscanf(s,"0x%16I64X",(__int64 *)&d) && strlen(s)>11) {flag=2;break;}
        if (1==sscanf(s,"0x%8X"    ,(  int   *)&f))                 {flag=1;break;}
        if (1==sscanf(s,"%f"       ,           &f)
         && 1==sscanf(s,"%lf"      ,           &d))                 {flag=3;break;}
    }
    if (flag&1) {
        printf("f=%g\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);
    }
    if (flag&2) {
        printf("\nd=%lg\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);
    }

    return 0;
}
//Input a float point number or 0xXXXXXXXX or 0xXXXXXXXXXXXXXXXX:0x3FC0000000000000
//
//d=0.125
//hex=3F C0 00 00 00 00 00 00
//bin=0011111111000000000000000000000000000000000000000000000000000000
//bin=0 01111111100   0000000000000000000000000000000000000000000000000000
//    + 1020  -1023 1.0000000000000000000000000000000000000000000000000000
//    + -3          1.0000000000000000000000000000000000000000000000000000
//
//Input a float point number or 0xXXXXXXXX or 0xXXXXXXXXXXXXXXXX:0x3E000000
//
//f=0.125
//hex=3E 00 00 00
//bin=00111110000000000000000000000000
//bin=0 01111100   00000000000000000000000
//    + 124 -127 1.00000000000000000000000
//    + -3       1.00000000000000000000000
//
//Input a float point number or 0xXXXXXXXX or 0xXXXXXXXXXXXXXXXX:0.125
//f=0.125
//hex=3E 00 00 00
//bin=00111110000000000000000000000000
//bin=0 01111100   00000000000000000000000
//    + 124 -127 1.00000000000000000000000
//    + -3       1.00000000000000000000000
//
//d=0.125
//hex=3F C0 00 00 00 00 00 00
//bin=0011111111000000000000000000000000000000000000000000000000000000
//bin=0 01111111100   0000000000000000000000000000000000000000000000000000
//    + 1020  -1023 1.0000000000000000000000000000000000000000000000000000
//    + -3          1.0000000000000000000000000000000000000000000000000000
//
//Input a float point number or 0xXXXXXXXX or 0xXXXXXXXXXXXXXXXX:
//

因为浮点数就是科学计数法呀，
就是一部分字节存精度，另一部分字节存指数
所以指数可以很大也可以很小，能表示的范围非常大，但是精度永远都是固定的

是负的38次方吧
https://blog.csdn.net/weixin_42130471/article/details/83869083

float是4个字节，遵循IEEE-754格式标准，在计算机中表示有三个部分组成：符号s 底数m 和 指数e。
float的m只有23位，2^23=8388608，总共有7位10进制数字，由于最左边的1省略了，所以表示的有效数字最高精确度位7～8位，包括整数部分，8位后的数字肯定不是准确的
https://www.cnblogs.com/buou/p/11144910.html