Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127. $$S : 1 \quad E : 10000001 \quad F : 11110000000000000000000$$ Here $S$, $E$ and $F$ denote the sign, exponent and fraction components of the floating point representation. The decimal value corresponding to the above representation (rounded to 2 decimal places) is ___________

In IEEE 754 single-precision floating point format, the value of a normalized number is given by:

From the given representation:

1. Sign bit ($S$): $S = 1 \implies (-1)^1 = -1$ (the number is negative).

2. Exponent ($E$): $E = 10000001_2 = 128 + 1 = 129$. The unbiased exponent is:

   $$e = E - \text{Bias} = 129 - 127 = 2$$

3. Fraction ($F$): $F = 11110000000000000000000_2$. The significand (mantissa with implicit leading bit) is:

   $$(1.F)_2 = 1 + 2^{-1} + 2^{-2} + 2^{-3} + 2^{-4} = 1 + 0.5 + 0.25 + 0.125 + 0.0625 = 1.9375$$

Now, calculate the decimal value:

Therefore, the decimal value is -7.75.