float is an IEEE 32 bit/4 byte floating point

 bit
-----
  31  = sign (0=positive,1=negative)
30-23 = 8 bit exponent (bias 7Fh)
22- 0 = 23 bit mantissa (no MS-bit;exponent adjusted)

////////\\\\\\\\////////\\\\\\\\
332        21        1
10987654321098765432109876543210
seeeeeeeemmmmmmmmmmmmmmmmmmmmmmm

80x06 reverse byte/word order         ,-hidden bit
                                      v
eg.               reverse  s eeeeeeee  mmmmmmm mmmmmmmm mmmmmmmm s ee mmmmmm
26.71875=00C0D541=41D5C000=0 10000011 h1010101 11000000 00000000=0 83 55C000
1000    =00007A44=447A0000=0 10001000 h1111010 00000000 00000000=0 88 7A0000
-1000   =00007AC4=C47A0000=1 10001000 h1111010 00000000 00000000=1 88 7A0000
0.05    =CDCC4C3D=3D4CCCCD=0 01111010 h1001100 11001100 11001101=0 7A 4CCCCD
-0.05   =CDCC4CBD=BD4CCCCD=1 01111010 h1001100 11001100 11001101=1 7A 4CCCCD

double is an IEEE 64 bit/8 byte floating point

 bit
-----
  63  = sign (0=positive,1=negative)
62-52 = 11 bit exponent (bias 3FFh)
51- 0 = 52 bit mantissa (no MS-bit;exponent adjusted)

////////\\\\\\\\////////\\\\\\\\////////\\\\\\\\////////\\\\\\\\
6  65        54        43        32        21        1
3210987654321098765432109876543210987654321098765432109876543210
seeeeeeeeeeemmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

80x06 reverse byte/word order                             ,-hidden bit
                                                          v
eg.                          reverse       s eeeeeee eeee  mmmm mmmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm s eee mmmmmmmmmmmmm
26.71875=0000000000B83A40=403AB80000000000=0 1000000 0011 h1010 10111000 00000000 00000000 00000000 00000000 00000000=0 403 AB80000000000
1000    =0000000000408F40=408F400000000000=0 1000000 1000 h1111 01000000 00000000 00000000 00000000 00000000 00000000=0 408 F400000000000
-1000   =0000000000408FC0=C08F400000000000=1 1000000 1000 h1111 01000000 00000000 00000000 00000000 00000000 00000000=1 408 F400000000000
0.05    =9A9999999999A93F=4FA999999999999A=0 1001111 1010 h1001 10011001 10011001 10011001 10011001 10011001 10011010=0 4FA 999999999999A
-0.05   =9A9999999999A9BF=BFA999999999999A=1 0111111 1010 h1001 10011001 10011001 10011001 10011001 10011001 10011010=1 3FA 999999999999A

Applesoft

Unpacked - 6 bytes

 bit
-----
47-40 = 8 bit exponent (excess $80;$80 is added to exponent)
39- 8 = 32 bit mantissa
 7- 0 = sign (MS-bit used only, bit7=0=positive, bit7=1=negative)

////////\\\\\\\\////////\\\\\\\\////////\\\\\\\\
4      43        32        21        1
765432109876543210987654321098765432109876543210
eeeeeeeemmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmssssssss

when number is negative, sign byte = first mantissa byte
when number is positive, sign byte = 0

eg.                   s eeeeeeee mmmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm
26.71875=85D5C0000000=0 10000101 11010101 11000000 00000000 00000000
1000    =8AFA00000000=0 10001010 11111010 00000000 00000000 00000000
-1000   =8AFA000000FA=1 10001010 11111010 00000000 00000000 00000000
0.05    =7CCCCCCCCD00=0 01111100 11001100 11001100 11001100 11001101
-0.05   =7CCCCCCCCDCC=1 01111100 11001100 11001100 11001100 11001101
                                 ^
Packed - 5 bytes                 `-always 1(usually hidden)

 bit
-----
39-32 = 8 bit exponent
31- 0 = sign bit + 31 bit mantissa (MS-bit=sign (0=positive;1=negative))

////////\\\\\\\\////////\\\\\\\\////////
3        32        21        1
9876543210987654321098765432109876543210
eeeeeeeesmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

eg.              eeeeeeee smmmmmmm mmmmmmmm mmmmmmmm mmmmmmmm
1000 =8A7A000000=10001010 01111010 00000000 00000000 00000000
-1000=8AFA000000=10001010 11111010 00000000 00000000 00000000
0.05 =7F4CCCCCCD=01111111 01001100 11001100 11001100 11001101
-0.05=7FCCCCCCCD=01111111 11001100 11001100 11001100 11001101
