Solve s=(1+F/2^11)2^E-16

$$s = ( 1 + \frac { F } { 2 ^ { 11 } } ) 2 ^ { E - 16 }$$

Solve for F

$$F=\frac{134217728s}{2^{E}}-2048$$

Steps for Solving Linear Equation

Calculate 2 to the power of 11 and get 2048.

$$s=\left(1+\frac{F}{2048}\right)\times 2^{E-16}$$

Use the distributive property to multiply 1+\frac{F}{2048} by 2^{E-16}.

$$s=2^{E-16}+\frac{F}{2048}\times 2^{E-16}$$

Express \frac{F}{2048}\times 2^{E-16} as a single fraction.

$$s=2^{E-16}+\frac{F\times 2^{E-16}}{2048}$$

Swap sides so that all variable terms are on the left hand side.

$$2^{E-16}+\frac{F\times 2^{E-16}}{2048}=s$$

Subtract 2^{E-16} from both sides.

$$\frac{F\times 2^{E-16}}{2048}=s-2^{E-16}$$

Multiply both sides of the equation by 2048.

$$F\times 2^{E-16}=2048s-2048\times 2^{E-16}$$

The equation is in standard form.

$$2^{E-16}F=2048s-2048\times 2^{E-16}$$

Divide both sides by 2^{E-16}.

$$\frac{2^{E-16}F}{2^{E-16}}=\frac{-\frac{2^{E}}{32}+2048s}{2^{E-16}}$$

Dividing by 2^{E-16} undoes the multiplication by 2^{E-16}.

$$F=\frac{-\frac{2^{E}}{32}+2048s}{2^{E-16}}$$

Divide 2048s-\frac{2^{E}}{32} by 2^{E-16}.

$$F=\frac{2048\left(65536s-2^{E}\right)}{2^{E}}$$

Solve for E

$$\left\{\begin{matrix}E=\log_{2}\left(\frac{s}{F+2048}\right)+27\text{, }&\left(s<0\text{ and }F<-2048\right)\text{ or }\left(s>0\text{ and }F>-2048\right)\\E\in \mathrm{R}\text{, }&s=0\text{ and }F=-2048\end{matrix}\right.$$