Show that in a base-beta floating-point number system the larger relative gap between two consecutive normalized numbers occurs between 1.000 ... 000 times beta^t and 1.000 ... 001 times beta^t. (The value of the exponent t is irrelevant.) Thus the largest relative error (the unit roundoff) occurs when one tries to represent the number that lies half way between these two. Show that the unit roundoff is 1/2 times beta^1-s, where beta is the number base, and s is the number of base-beta digits in the significant. Show that in a base-beta floating-point number system the larger relative gap between two consecutive normalized numbers occurs between 1.000 ... 000 times beta^t and 1.000 ... 001 times beta^t. (The value of the exponent t is irrelevant.) Thus the largest relative error (the unit roundoff) occurs when one tries to represent the number that lies half way between these two. Show that the unit roundoff is 1/2 times beta^1-s, where beta is the number base, and s is the number of base-beta digits in the significant