Can an exponent be stored as a floating point number? - binary

Question

I would like to know if a binary exponent can be stored in floating point form. Here is a example of what I mean:
In a system floating point numbers use a 10-bit two's complement mantissa and a 6-bit floating point exponent
Convert 0101001000 000100 into denary:
Well if I assume that the exponent is in normal binary, the exponent equals 4
So the decimal point in the mantissa goes here initially:
0.101001000
Then we move the decimal point 4 places to the right, yielding
01010.01
Which equals 10.25 in denary.
This answer will be wildly different if the exponent can be stored as with a decimal. I am asking if the exponent can be stored in this way.

Answer 1

if a binary exponent can be stored in floating point form
Yes.
To form the denary from a string, use strtol().
To covert the denary into a floating-point, extract the bits into its "mantissa" and exponent. Form the FP value with ldexp().
double ldexp(double x, int exp);
The ldexp functions multiply a floating-point number by an integral power of 2.
c11dr §7.12.6.7 2
#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#define denary_MANIISSA_EXPO 9
#define denary_MANIISSA_MASK 0xFFC0u
#define denary_EXPO_SCALE 64
double denary_to_double(denary d) {
int expo = d & (denary_EXPO_SCALE - 1);
int mantissa = (d - expo) / denary_EXPO_SCALE;
return ldexp(mantissa, expo - denary_MANIISSA_EXPO);
}
void denary_test(const char *s) {
denary d = (denary) strtol(s, NULL, 2);
printf("0x%04X -->", d & 0xFFFF);
printf(" %+.9f\n", denary_to_double(d));
}
int main(void) {
denary_test("0101001000" "000100");
denary_test("0000000000" "000000"); // zero
denary_test("0000000001" "000000"); // denary_POS_MIN
denary_test("1111111111" "000000"); // denary_NEG_MIN
denary_test("0111111111" "111111"); // denary_POS_MAX
denary_test("1000000000" "111111"); // denary_NEG_MAX
}
Output
0x5204 --> +10.250000000
0x0000 --> +0.000000000
0x0040 --> +0.001953125
0xFFC0 --> -0.001953125
0x7FFF --> +9205357638345293824.000000000
0x803F --> -9223372036854775808.000000000