1. Round-off error results when a machine that stores numbers using finite bits performs floating point operations involving numbers of greatly different magnitude. Consider a machine that stores numbers as base 10 (B = 10) with 5 digits for the mantissa (aka the significand) and 1 digit for the exponent. (Note: technically there antissa there would also be an additional 1 bit reserved for the sign of the mantissa and one bit for the sign of the exponent.) (5pts) sulect result fro024, (a) Compute the roundoff error that would result from the following operation: 1.7421485.3 (3pts) (b) Compute the relative error that results from this operation. (1pt) (c) Compute the machine precision: € = B-(p-1), where p is the width of the mantissa. Note the similarity in magnitude between this quantity and the result from part b. (1pt)

Decode the number using the given private key. Decode the number M = 38 using the private key d = 17 and n = 77. Assume you are decoding the number using the RSA cryptosystem. Note: You can use the Modular Exponentiation calculator to help with the calculation.

PROBLEM 4 Solve the following problems: (a) How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his 25 employees? (b) A state's license plate has 7 characters. Each character can be a capital letter (A – Z), or a non-zero digit (1 – 9). How many license plates start with 3 capital letters and end with 4 digits with no letter or digit repeated? (c) How many binary strings of length 5 have at least 2 adjacent bits that are the same ("00" or "11") somewhere in the string?

a)Select a variety of one- and two digit numbers between 1 and 99 and multiply by 9. Record your results. b) Find the sum of the digits in each of your products in part (a). If the sum is not a one digit number find the sum of the digits of the resulting sum again until you obtain a one -digit number, c) make a conjecture about the sum of digits when a one- or two digit number is multiplied by 9