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 $0\text{}\text{}\le i\le 3$, 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”.