Assignment Set - 1

Please write your Roll Number, Name and Assignment Number at the header of each program.

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Assignment 1.a:        Filename: a1a.c

(a) Write a program that reads in a number A in decimal, converts it to base-4 and prints the digits in base-4.
     The digits may be printed in reverse order, that is, with the least significant bit (LSB) first.

(b) Augment the above program to also read in a number B in octal and print it in decimal.

Hint: The following code fragment prints the decimal digits from an integer n. Which digit is printed first, LSB or MSB?

        while (n > 0)
    {
        lsb = n % 10;
        printf("%d ", lsb);
        n = n / 10;
    }

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Assignment 1.b:        Filename: a1b.c

Consider the following equation:

    ( x² - 10x + 16 )( log₄ x - 2 ) = 0

Write a program that uses the bisection method (discussed in the tutorial class) to find a root of the above equation in each of the following intervals: [0, 5], [5, 10], [10, 20]

Notable Issues:

1. Look up the library functions for computing logarithms. How can use express a logarithm of arbitrary base in terms of natural logarithms?
2. When you use math library functions, please remember: # include <math.h> and compile with cc <file-name> -lm

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Assignment 1.c:        Filename: a1c.c

A ball is thrown vertically upwards with an initial velocity of 60 km/h. Following this, the ball bounces on the ground repeatedly. The kinetic energy of the ball after each bounce becomes half of its kinetic energy before the bounce.

Write a program that computes and prints the following (assume g = 9.8 m/s²):

(a) The maximum height to which the ball rises before returning to ground in the first 10 iterations

(b) The total time spent before it hits the ground for the 10^th time

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