Question: MAPLE TA TEST about floating-point arithmetic

Consider a "toy system" of floating-point arithmetic where each floating-point numberis of the form
x = (-1)^s × (1 + m) × 2^e-σ:

The mantissa is a binary number such that
m = 0:m₁m₂m₃ (base 2) belongs to [0; 1)

and the exponent e is a binary integer such that
1 ≤ e = e₃e₂e₁e₀ (base 2) ≤ 14:

Each m_j and e_j is either 0 and 1; similarly s belongs to {0,1}  The shift is σ = 7.

The answers in this question must be written as decimal numbers (base 10) and must be exact at least to 6 decimal places.
(1) Compute the following quantities:
a) the number of bits of memory that each number occupies;
b) the machine epsilon;
c) the greatest positive floating-point number;
d) the smallest positive floating-point number greater zero.
(2) List the floating-point numbers x in the interval 2 < x < 4 in ascending order, excluding 2 and 4.