Explain IEEE standard for floating point numbers.OR How floating point numbers are represented in computer, also give IEEE 754 standard 32-bit floating point number format.

1.The IEEE standard for floating point arithmetic (IEEE 754) is a technical standard for floating point computation.

2. IEEE 754 numbers are divided into two types :

a. Single precision :

i. The floating point numbers in 32-bit are single precision.

ii. 32-bit floating point number in single precision is represented as + 1M × 2^E .

iii. The relationship between E and E’ in single precision is given as E’ = E + 127.

iv. The 8-bit assigned for exponent E’ (Modified exponent) is in the range 0 < E’ < 255 for normal values. Thus the actual exponent is in the range – 127 ≤ E ≤ 127.

v. The values 0 and 255 are used to indicates the floating points values of exact 0 and infinite respectively.

b. Double precision :

i. The floating number in 64-bit are double precision. image show the double precision format of IEEE standard form.

ii. The double precision format has increased, exponent and mantissa ranges.

iii. The 11 bit assigned for exponent E’ has range 0 < E’ < 2047 for normal values. Thus the actual exponent E is in the range – 1022 ≤ E ≤1023. The relationship between E and E’ in double precision is given as E’ = E + 1023.

iv. The 52 bit is assigned for mantissa, provides a precision equivalent to about 16 decimal digits.

v. 64-bit floating point number in double precision is represented as ± 1.M × 2^E . image Double precision.