Suppose a new standard MAE38416 is defined to store floating

Suppose a new standard MAE384-16 is defined to store floating point numbers using 16 bits. The first bit is used to store the sign as in IEEE-754, the next 6 bits store the exponent plus the bias (bias = 31), and the remaining 9 bits store the mantissa. As in IEEE-754, an exponent of all zero bits is used to indicate true zero, and an exponent of all one bits is used to store +/- infinity. Determine by hand in decimal format a) the smallest possible non-zero positive number: b) the largest possible finite positive number; c) the smallest possible difference between the number 1.0 times 10 degree and the next larger possible number. Problem 3 required submission: Handwritten (or printed) all steps to obtain the answers, incl. the final answers.

Solution

Solution :

Part A)

realmin:

Smallest positive normalized floating-point number

Syntax

n = realmin
realmin(\'double\')
realmin(\'single\')

Description

n = realmin returns the smallest positive normalized floating-point number in IEEE double precision.

realmin(\'double\') is the same as realmin with no arguments.

realmin(\'single\') returns the smallest positive normalized floating-point number in IEEE single precision.

Examples

Find the value of the constant realmin:

Part B)

realmax

Largest positive floating-point number

Syntax

n = realmax

Description

n = realmax returns the largest finite floating-point number in IEEE double precision.

realmax(\'double\') is the same as realmax with no arguments.

realmax(\'single\') returns the largest finite floating-point number in IEEE single precision.

Examples

Find the value of the constant realmax:

Largest and Smallest Single-Precision Values

The MATLAB functions realmax and realmin, when called with the argument \'single\', return the maximum and minimum values that you can represent with the single data type:

Numbers larger than realmax(\'single\') or smaller than -realmax(\'single\') are assigned the values of positive and negative infinity, respectively: