Question

The value encoded by a given IEEE 754 bit representation can be divided into how many cases?

1) 1 case
2) 2 cases
3) 3 cases
4) 4 cases

Answer 1

The IEEE 754 bit representation divides encoded values into four cases: normalized values, denormalized values, zero, and special cases like infinity and NaN (Not a Number).

Step-by-step explanation:

The value encoded by an IEEE 754 bit representation can actually be divided into four cases. The IEEE 754 standard is used for representing floating-point numbers in computers and it specifies the format for single precision, double precision, and more recently, half precision formats. The four cases can be described as follows:

• Normalized values: These involve a non-zero exponent and a fractional part (mantissa). In this case, the value is represented with an implied leading 1 before the binary point.
• Denormalized values: These occur when the exponent is zero, and the mantissa is non-zero, which allows for the representation of numbers closer to zero than what is possible with normalized values.
• Zero: This is a special case in which both the exponent and the mantissa are zero, representing the number zero.
• Infinity and NaN (Not a Number): These are special cases used to represent values that result from operations that have undefined or unrepresentable results within the real numbers, such as division by zero or invalid operations.