1. YOUR VIRTUAL WORLD – THE HEXADECIMAL NUMBERING SYSTEM Prepared by Mrs. Christina Morris, July, 2014

2. HEXADECIMAL NUMBER SYSTEM CONVERSION ➢ Our Objective today – Students will be able to convert values to and from the hexadecimal number system from decimal and binary, and understand how data is represented and stored on a computer. ➢ What are the numbering systems we’ve covered so far? ➢ Decimal ➢ Binary

3. LET’S GET STARTED - ➢ Define Binary Math. ➢ Explain the process of how we converted Decimal math items to Binary. ➢ State the algorithm to convert a number to or from decimal or binary.

4. LET’S MOVE ON - ➢ Hexadecimal numbers are base 16 math. ➢ How does it work? (class examples) ➢ Practice – let’s convert some numbers – ➢ Student Worksheet – Let’s take a few minutes and complete this worksheet.

5. Example #1 137 in base 10 is equal to each digit multiplied with its corresponding power of 10: 137 10 = 1 x 100 + 3 x 10 + 7 x 1 = 1×10 2 +3×10 1 +7×100 = 100+30+7 Hex numbers are read the same way, but each digit counts the power of 16 instead of power of 10. Multiply each digit of the hex number with its corresponding power of 16.

6. Example #1 37 in base 10 is equal to each digit multiplied with its corresponding power of 10: 137 10 = 1 x 100 + 3 x 10 + 7 x 1 = 1×10 2 +3×10 1 +7×100 = 100+30+7 Hex numbers are read the same way, but each digit counts the power of 16 instead of power of 10. Multiply each digit of the hex number with its corresponding power of 16.

7. Example #2 3B in base 16 is equal to each digit multiplied with its corresponding power of 16: 3B = 3×16 1 +11×16 0 = 48+11 = 59

8. Example #3 E7A9 in base 16 is equal to each digit multiplied with its corresponding power of 16: E7A9 = 14×16 3 +7×16 2 +10×16 1 +9×16 0 = 57344+1792+160+9 =59305

9. HOW ARE THE NUMBERING SYSTEMS USED IN COMPUTER SCIENCE? ➢ Binary ➢ Octal - early computing by 12- and 24- bit processors – to abbreviate binary digits. ➢ Hexadecimal - http://www.linfo.org/hexadecimal.html and http://digiassn.blogspot.com/2006/02/why- do-we-use-hexadecimal.html http://www.linfo.org/hexadecimal.html http://digiassn.blogspot.com/2006/02/why- do-we-use-hexadecimal.html

10. SUMMARY - ➢ What is the algorithm for converting number vales between the various numbering systems of binary, decimal and/or hexidecimal? ➢ Explain how various numbering systems are employed in computer science.