MATH 22 DAC Discrete Mathematics Algorithm Converts Decimal to Binary Program

Computer Science

math 22

De Anza College

MATH

Question Description

The following algorithm converts decimal to binary using repeated division by 2. Write a program using any programming language to execute repeated division by 2.

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The following algorithm converts decimal to binary using repeated division by 2. Write a program using any programming language to execute repeated division by 2. Input: n [a nonnegative integer] Algorithm Body: q := n, i := 0 [Repeatedly perform the integer division of q by 2 until q becomes 0. Store successive remainders in a one-dimensional array r [0], r [1], r [2], . . . , r [k]. Even if the initialvalue of q equals 0, the loop should execute one time (so that r [0] is computed ). Thus the guard condition for the while loop is i = 0 or q  = 0.] while (i = 0 or q  = 0) r [i] := q mod 2 q := q div 2 [r [i] and q can be obtained by calling the division algorithm.] i := i + 1 end while [After execution of this step, the values of r [0], r [1], . . . , r [i − 1] are all 0’s and 1’s, and a = (r [i − 1]r [i − 2] · · · r [2]r [1]r [0])2 .] Output: r [0], r [1], r [2], . . . , r [i − 1] [a sequence of integers] ...
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