a-) What is the representation of the number $(12.31)_{10}$ in the F (3,3,4,4) system?
b-) How many numbers can we represent in the floating point system F(3,3,4,4) ?
c-) How many numbers can we represent in the floating point system F (6,3,4,5) ?
d-) What is the representation of the number $(0,4)_{10}$ in the F (4,5,2,3) system?
e-) What is the largest positive number represented in the floating point system F (4,5,2,3) in decimal base?
I did the following
a-) As we have base = 3, significant figures = 3 and exponents ranging from -4 to 4, so when dividing 12 by 3 we get 4 and remainder 0 dividing again 4 by 3 we get 1 and remainder 1, so we have 12 in the base 3 is 110. For the 0.31 in base 3, I multiplied 0.31 by 3 got 0.91 took 0 and multiplied 0.91 by 3 with result 2.73 took 2 and multiplied 0.73 by 3. Continuing with the procedure we have that 0.31 = 0.02210022.. ..
So the numerical representation is 0.110 x $3^3$
b-)
The numbers can be positive or negative ie 2 options.
Of the 3 digits the first ($d_1$) can be 2 (cannot be 0) can be 1 and 2. $d_2$ can be the 3 (0,1,2).
$d_3$ can be the 3 (0,1,2).
exponents range from -4 to 4 so can be -4, -3, -2, -1, 0 , 1, 2, 3, 4 = 9 options.
So we have 2 x 2 x 3 x 3 x 9 +1 (the 0) = 325
c-)
Using the same procedure as in the previous exercise, I got 361 = 2 x 2 x 3 x 3 x 10 +1
d-)
Using the same procedure performed in item a, we have that $(0,4)_{10}$ = 0.12121 x $4^0$.
e-)
As the exponents vary from -2 to 3 the base is 4 and the number of significant digits is 5 so we have that the largest number will be as follows $0.d_1d_2d_3d_4d_5$ x $4^3$ where $d_1,d_2,d_3,d_4,d_5$ will be the largest possible number, that is, 3. So we have the following number 0.33333 x $4^3$ = 333.33 which in base 10 is 63.9375.
The exercises have alternatives and it matches, except for c-) which doesn't have an alternative that matches my answer.
Are the answers correct?
Thank's for any help