1 / 17

Counting Systems

Counting Systems. Mr. Bigham. Warm-up: When Does. 9 + 4 = 1 30 + 5 = 4 1 + 1 = 10. ?. If the clock reads 9, what time will it be if you add 4 hours? If the day is January 30 th what day will it be if in 5 more days? How do computers count to two? (Binary). Decimal System.

angeni
Download Presentation

Counting Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Counting Systems Mr. Bigham

  2. Warm-up:When Does 9 + 4 = 1 30 + 5 = 4 1 + 1 = 10 ?

  3. If the clock reads 9, what time will it be if you add 4 hours? If the day is January 30th what day will it be if in 5 more days? How do computers count to two? (Binary)

  4. Decimal System

  5. Why base 10? • Does it 10 have special mathematical properties that make it a better base? • “Counting in tens is a biological accident.”– Professor Zirkel, Dozenal Society of America • What other bases are used? • What are the advantages and disadvantages of different bases?

  6. Mayan base 20 (Vigesimal)

  7. In dozenal counting we use twelve symbols, adding two digits to represent ten and eleven since 10 still represents the base. • In dozenal counting he numeral 342 represents • 3H(twelve)^2 + 4H(twelve) + 2. • Thus 342 in dozenals represents 482 in the familiar awkward decimal base. • Many people use X and # to represent the digits for ten and eleven. They are pronounced dekand el.

  8. Babylonian Counting “Babylonians were the one civilization that intelligently developed a number base – base sixty. If twelve has the advantage of the factors 2, 3, 4, and 6, sixty has 2, 3, 4, 5, 6, 10 12, 15, 20, and 30.” -Professor Zirkel

  9. Binary (base 2 counting)

  10. Hexadecimal (base 16)

  11. Exercise Translate the numeral 10010: • From base twenty (Mayan) • Base 12 (dozenal) • Base 2 (binary) • Base 16 (hexidecimal) • A base of your choosing Translate the numeral 42 into different bases using radix notation. Example: 42 = 11203 = 2224 = ?

  12. Coding Coding converts messages to numbers and back. Can you decode the message below? A zero is used for space. 20 8 9 19 0 9 19 0 1 12 1 13 5 0 3 15 4 5

  13. Coding Complications • If you have a decimal coded message: 202 does it decode to bob or tb? To avoid confusing when two digits refer to a two letters or one, all letters are coded using 2 digits. i.e. A = 01, B = 02, G = 07, space = 00. Decode: 04150021002114041920011404?

  14. How many digits needed? • For base ten coding two digits were needed to make enough numerals to correspond to all the letters of the alphabet. How many total symbols could you code with two base ten digits? • How many binary (base two) digits would you need to code the alphabet? • How many hexadecimal digits would you need to code 250 symbols?

  15. ASCII Code • Most computers use an eight digit (bit) binary code to represent letters and symbols. • The first three digits give information about what type of symbol (number, punctuation, capital, lower case etc.) • If the first three digits are 010, it is a upper case letter. If it is 011 it is lower case. The last 5 digits can be converted to decimal and associated with the normal alphabet key.

  16. Examples 01001000 = H The 010 signals capital letter. The 01000 equals 8 in binary counting. Eight is associated with the letter h in the standard alphabet key. 01101001 = i The 011 signals lower case letter. The 01001 equals 9 in binary counting. Nine is associated with the letter I in the standard alphabet key.

  17. Exercises • Decode the following two digit hexadecimal coded message: 04090400190F15000C0501120E00 130F0D051408090E07? • Code a message using a base of your choosing.

More Related