# Like FCF, a Functional Continued Sum (FCS) #F_(fcs)(x; a) = F(x+a (F(x + a (F(x + a(F...))))#. With binary x and y, #y = log_2(x; 1) = log_2(x + log_2(x+log_2(x+...)))#. How do you find the binary at x = (101)_2?

##### 2 Answers

#### Explanation:

It is given that

From this, we can see that

Now, it is further given that

Then, assuming that

#### Explanation:

The inverting, #2^y = log_2 ^(-1)(log_2( x + y ) = x +y ), and so,

For #x = 5 =(101), y = 3 = (11)_2, as 2^3-3 = 5 (QED).

When

method. For more sd, use numerical iterative method for

approximating the solution.

Graphical solution:

As

graph{(x-2^y+y)(x - 3)(x+y)=0}

Locating the root near

graph{(x -2^y+y)(x-3)=0[2.999 3.0009 2.444 2.447]}