For the IEEE Std 754-1985 single precision floating point number, based on the d
ID: 3775948 • Letter: F
Question
For the IEEE Std 754-1985 single precision floating point number, based on the definition, it has 32 bits in total: 1 sign bit, 8 bits for Exponent and 23 bits for Fraction. Exponents 00000000 and 11111111 are reserved. Here are questions: What is the scope of Exponents if we don't consider about the reserved part?(Give the formula will be fine.) What is the scope of ?Exponent-bias? if we don't consider about the reserved part?(Give the formula will be fine.) What is the scope of fraction part?(Give the formula will be fine.) What is used to represent 0 in IEEE Std 754-1985 single precision floating point number? What is used to represent +infinity in IEEE Std 754-1985 single precision floating point number? What is the smallest positive value?(Give the formula will be fine.)Explanation / Answer
Answer
a.
The scope of Exponents if we don't consider about the reserved part depends on the number of bits used for the exponent part. As given, 8 bits are used for the exponent part, the largest number that can be stored in the exponenet is 28-1 - 1 = 127 and as this has sign bit also, the overall scope of the exponenet will be -128 to +127.
b.
Scope of exponent bias is 0x7F = 127 (i.e. 28-1)
c.
The scope of fractional part is log10(224)
Though only 23 bits of fraction appear in the memory format, but the total precision is 24 bits.
d.
0 is not directly representable in the straight format, due to the assumption of a leading 1 and a true 0 mantissa needs to be specified in order to yield a value of 0. 0 is a special case which is denoted with an exponent field of all zero bits, and a fraction field of all zero bits. Also, 0 and +0 are distinct values, though they both may be compared as equal.