-4 as floating point
AFAIK, there is no standard with that format.

You can nevertheless try to imitate the old MIL-STD-1750A floating point format, which had two's complement mantissas and exponents.

The two's complement mantissa range is -1.0 to 0.999999....

Something like that :

                     Mantissa Exponent
'   0 =                  0000 0000
'0.25 =  0.5 * 2**-1 =   0100 1111
' 0.5 =   0.5 * 2**0 =   0100 0000
'  +1 =   0.5 * 2**1 =   0100 0001
'  +2 =   0.5 * 2**2 =   0100 0010
'  +4 =   0.5 * 2**3 =   0100 0011
'  -1 =  -1.0 * 2**0 =   1000 0000
'  -2 =  -1.0 * 2**1 =   1000 0001
'  -4 =  -1.0 * 2**2 =   1000 0010


Note the asymmetry between +1 and -1.

etc...