Question

Describe how zero, infinity, and NaN are stored in IEEE 754 floating point formats

Answer 1

IEEE 754 standards:

· This is a technical standard for floating point operations.

· Established in the year 1985

· By, IEEE, the Institute of Electrical and Electronics Engineers

· IEEE has reserved some values for solving the uncertainty issues.

· They are ZERO, INFINITY, NaN

According to IEEE 754, the floating points numbers are represented using 3 components:

1. Sign of mantissa

           This is to denote whether the floating point number is a positive or a negative number.

0 represent positive numbers, while 1 represent a negative number.

2. Exponent field:

This field is to represent the negative and positive exponents of the floating point number.

3. Mantissa:

This field has all the significant digits of the floating point number represented.

Also these fields are only filled with binary values, 0 and 1.

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ZERO:

· Here the exponent and mantissa are filled with value 0

· According to this standard, +0 and -0 are distinct, even if they have equal value.

· The sign bit varies for the + and – infinity.

The bit representation of zero can be like:

+0.0 = 0 00000000 00000000000000000000000

-0.0 = 1 00000000 00000000000000000000000

INFINITY:

· Here exponents are all 1’s

· Mantissa all 0’s

· The +infinity and – infinity are represented distinctively

· The sign bit value helps to identify whether it’s positive or a negative infinity.

The bit representation of two kinds of infinity are:

+Infinity= 0 11111111 00000000000000000000000

- Infinity = 1 11111111  00000000000000000000000

NaN:

· Not-A-Number

· This is to represent an error number value.

· NaN, can be the results of operations like 0/0, infinity/infinity, infinity-infinity, or infinity*0.

· Here exponent fields are all 1, with 0 sign bit

· mantissa with 1 followed by all zeros

· there are different kinds of NaN like, Quiet NaN or qNaN

· and also Signalling NaN or sNaN

. the bit representation of common NaN is like:

Nan= 0  11111111 10000000000000000000000

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