Int num = 25; String bin = \"\" ; int remainder = num; while (remainder ! = 0) {

Question

Int num = 25; String bin = "" ; int remainder = num; while (remainder ! = 0) { bin = (remainder % 2) + bin; remainder = remainder / 2; } System.out.println(num + " = " + bin); Complete the trace table below for the code segment in Listing 3. Use a question mark (?) to indicate that the value is unknown and a dash (-) to indicate that the value of the variable has not been modified. Also, give the value of the Boolean expression remainder! = 0 each time it is evaluated. The first line of the trace table has been completed showing the values of these expressions prior to the first iteration of the loop. What would the code segment output?

Explanation / Answer

(a)

The required trace table for every loop iteration is as above. Here, all the values are known so there should not be ?s in the table.

Here, at each iteration, the remainder is calculated by dividing the number by 2 and this remainder (either 0 and 1) is written in the front of bin variable.

For example, in the first step, 25 % 2 = 1 and as num as well as remainder variables are defined as int, the division 25 / 2 becomes 12 instead of 12.5. So, as both of them are int, the value after decimal place is simply discarded.

On the second iteration, 12 % 2 becomes 0. So,0 is inserted in the starting of bin variable. So, bin = "01". (“0” + “1” = “01”. + operator between 2 strings works as a concatenation operator so.. .)

This process continues till we get false for remainder != 0. In this last step, 1 / 2 is done which means 0.5 for float and 0 for int. So, remainder becomes 0 and the loop is terminated.

(b)

The code segment output line is : 25 = 11001

In general terms, this code segment is giving the binary representation of a decimal number "num" inside "bin" variable. So, you can verify this with output also. (11001)2 means (25)10.

num bin remainder remainder != 0 25 25 true - "1" 12 true - "01" 6 true - "001" 3 true - "1001" 1 true - "11001" 0 false

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