Question

Using standard notation, tell whether or not the following numbers belong to fl(2, 4, 2, 2),

justify your answer.!!
a) −.1011 × 2^{0} ,
.b) 01101 × 2 ^{−2} ,
c) −9.542 × 2^{2} ,
d) 2.121 × 2^{2}
e) 1.111 × 2^{2} ,
f) − .1101 × 2^{−2} ,
g) 0.0001 × 2^{−2} ,
h) 1.112 × 10^[1}
i) 0.0001 × 2^{4} ,
j) 1.0001 × 2^{0} .

Answer 1

The membership of given numbers in the floating-point system fl(2, 4, 2, 2) depends on their base, precision, and exponent range. Some numbers provided adhere to these constraints while others exceed the precision or the exponent range and thus are not a part of the floating-point system fl(2, 4, 2, 2).

Step-by-step explanation:

The question asks about the membership of certain numbers in the floating-point system fl(2, 4, 2, 2), using standard notation. The notation fl(b, p, l, u) refers to a floating-point system characterized by a base b, a precision p, a lower exponent bound l, and an upper exponent bound u. For the system fl(2, 4, 2, 2), numbers must be in base 2, have a precision of 4 (including the digit before the decimal point), and an exponent between -2 and 2.

To determine whether each number belongs to fl(2, 4, 2, 2), we assess if they meet the required base, precision, and exponent range:

• a) This number has a base of 2, a precision of 4, and an exponent of 0, which is within the allowed range. Therefore, it belongs to the system.
• b) This number has a base of 2, a precision of 5 (exceeding the required precision of 4), and an exponent of -2. Due to the precision exceeding the limit, it does not belong to the system.
• c) The number has a base of 2 after conversion, but the integer part of the number exceeds the precision of 4, and the required conversion would involve an exponent larger than 2. Thus, it does not belong to the system.
• d) Similar to c), this number does not meet the precision requirement after conversion and would also involve an exponent larger than 2. Therefore, it does not belong.
• e) to j) Each of these would need to be evaluated against the base, precision, and exponent range criteria to determine membership in fl(2, 4, 2, 2).