Decimal and hexadecimal representation of different powers of 2: When a value “x” is a power of 2, that is x = 2 n for some nonnegative integer n. Here, the binary representation of x is basically “1” followed by n zeros. The hexadecimal digit is represented by “4” zeros. Hence, the format for “n” is “i + 4j”. From “i + 4j” format, where 0 ≤ i ≤ 3 , user can write “x” with a leading hex digit of 1, 2, and 3 and then followed by “j” hexadecimal digits. If “i = 0”, then hex digit is “1”. If “i = 1”, then hex digit is “2”. If “i = 2”, then hex digit is “4”. If “i = 3”, then hex digit is “8”. Example: The example for decimal and hexadecimal representation of power of “2” is shown below: Here assume x = 2048 = 2 11 . Now, write the “n” value as the format of “i + 4j” that is “3 + 4.2”. From the given format, the “i” value of “3” in hexadecimal is “8”. Then “j” is “2” so, after “8” two 0’s followed. Hence, the hexadecimal value is “0x800”.

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Chapter 2.1, Problem 2.2PP

Program Plan Intro

Decimal and hexadecimal representation of different powers of 2:

When a value “x” is a power of 2, that is x = 2ⁿ for some nonnegative integer n.

Here, the binary representation of x is basically “1” followed by n zeros.

The hexadecimal digit is represented by “4” zeros. Hence, the format for “n” is “i + 4j”.

From “i + 4j” format, where 0 ≤ i ≤ 3, user can write “x” with a leading hex digit of 1, 2, and 3 and then followed by “j” hexadecimal digits.

If “i = 0”, then hex digit is “1”.

If “i = 1”, then hex digit is “2”.

If “i = 2”, then hex digit is “4”.

If “i = 3”, then hex digit is “8”.

Example:

The example for decimal and hexadecimal representation of power of “2” is shown below:

Here assume x = 2048 = 2¹¹.

Now, write the “n” value as the format of “i + 4j” that is “3 + 4.2”.

From the given format, the “i” value of “3” in hexadecimal is “8”. Then “j” is “2” so, after “8” two 0’s followed. Hence, the hexadecimal value is “0x800”.

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