Chapter 2.1, Problem 2.3PP

Program Plan Intro

Conversion between decimal and hexadecimal:

• Using multiplication or division, users can make the conversion between the decimal and hexadecimal.
• To convert a decimal number “x” to hexadecimal, users can repetitively divide “x” by “16”, providing a quotient “q” and a remainder “r”, such that “x = q*16 + r”.
  • Then use the hexadecimal digit representing “r” as the least significant digit and create the remaining digits by repeating the procedure on “q”.
• To convert a hexadecimal number to decimal number, users need to multiply each of the hexadecimal digits by the appropriate power of “16”.

Example:

The example for converting decimal number “142482” to hexadecimal is shown below:

$\begin{array}{l}142482=8905\times 16+2\left(2\right)\\ 8905=556\times 16+9\left(9\right)\\ 556=34\times 16+12\left(C\right)\\ 34=2\times 16+2\left(2\right)\\ 2=0\times 16+2\left(2\right)\end{array}$

Hence, the hexadecimal representation for “142482” is “0x22C92”.

The example for converting the hexadecimal of “0x8AE” to decimal number is shown below:

$\begin{array}{l}\text{0x8AE}=8\times {16}^2+10\times {16}^1+14\times {16}^0\\ =8\times 256+10\times 16+14\times 1\\ =2048+160+14\\ =2222\end{array}$

Hence, the decimal value for “0x8AE” is “2222”.