1. Binary Conversions Number systems Binary to decimal Decimal to binary

2. Binary Humor There are 10 kinds of people in the world - those who understand binary and those who don't.

3. Numbering Systems Base 10 or decimal numbering system  Base-10 numbering systems dictate that the numbering scheme begins to repeat after the tenth digit (in our case, the number 9).  Zero is always the first number.  When we count, we usually count "00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 11, 12,...“

4. Numbering Systems Base 10 or decimal numbering system  Each digit to the left and right of the decimal point is given a name which identifies that digit's placeholder.  Each placeholder is a multiple of ten.  For now lets just consider positive numbers.

5. Numbering Systems - Base Ten Each placeholder is a base of ten. 10º = ones  Any number to the zero power is always equal to 1.  nº=1  10º=1 10¹ = tens  Any number to the first power is always equal itself.  n¹=n  10¹=10 10² = hundreds 10³ = thousands THOUSANDSTHOUSANDS HUNDREDSHUNDREDS TENSTENS ONESONES 7408

6. Numbering Systems – Base Ten Arithmetic expression of 8 in 7408. Work right to left of decimal point. The ones position in expanded notation calculating the exponent.  10º*8=8 is the same as 1*8=8

7. Numbering Systems – Base Ten Number7408 Position Name ThousandsHundredsTensOnes Exponential Expression 10³*710²*410¹*010º*8 Calculated Exponent 1000*7100*410*01*8 Sum of the powers of ten. 1000*7 + 100*4 + 10*0 + 1*8 = 7408

8. Numbering Systems – Base two Binary system is based on multiples of two. In binary numbering the numbering scheme repeats after the second digit. Let's count to five in binary: “0000, 0001, 0010, 0011, 0100, 0101“ Binary numbering includes names for digit placeholders.

9. Numbering Systems – Base two Picture a odometer that is only capable of counting to two.

10. Numbering Systems – Base two Binary placeholders  Ones  Twos  Fours  Eights  Sixteen's  Thirty-twos  Sixty-fours Decimal placeholders  Ones  Tens  Hundreds  Thousands  Ten-thousands  Hundred-thousands  Millions

11. Numbering Systems – Base two If the binary system is based on powers of 2, why is there still a "ones" position? Remember: Anything to the zero power is always equal to 1. In binary, the "ones" position is represented by the exponential expression 2º.

12. Convert Binary to Decimal Sum of the powers of two. 8*1 + 4*1 + 2*0 + 1*1 = 13 Number1101 Position Name EightsFoursTwosOnes Exponential Expression 2³*12²*12¹*02º*1 Calculated Exponent 8*14*12*01*1

13. Convert Binary to Decimal Step 1 - Write the binary number in a row, separating the digits into columns. Number 1101

14. Convert Binary to Decimal Step 2 - I want to decide whether each digit placeholder is "ON" or "OFF.“ "1" is "ON" and a "0" is "OFF.“ We don't have to calculate any digit placeholders that are turned off. Number1101 ON/OFFOn OffON

15. Convert Binary to Decimal Step 3 - Write the exponential expressions ("powers of two") that represent each placeholder and multiply each expression by 1. We do this only for the placeholders that are turned ON. For the placeholders which are turned OFF, we simply bring down the zero from the number itself Number1101 ON/OFFOn OffON Exponential Expression 2³*12²*102º*1

16. Convert Binary to Decimal Step 4 - Calculate the exponents to get a simple multiplication expression for each placeholder. Number1101 ON/OFFOn OffON Exponential Expression 2³*12²*102º*1 Calculated Exponent 8*14*101*1

17. Convert Binary to Decimal Step 5 - Solve the multiplication expressions from step #4. Number1101 ON/OFFOn OffON Exponential Expression 2³*12²*102º*1 Calculated Exponent 8*14*101*1 Solved Multiplication 8401

18. Convert Binary to Decimal Step 6 - Add all the multiplication answers from step #5 together to get our decimal number Number1101 ON/OFFOn OffON Exponential Expression 2³*12²*102º*1 Calculated Exponent 8*14*101*1 Solved Multiplication 8401 Add to calculate Value 8+4+0+1=13

19. Convert Binary to Decimal Example Number101101 ON/OFFOnOffOn OffOn Exponential Expression 2525 02³2³2²2²02º*1 Calculated Exponent 32*108*14*101*1 Solved Multiplication 3208401 Add to calculate Value 32+0+8+4+0+1=45

20. Covert Decimal to Binary Step 1 - Take the decimal number and divide it by 2. Important: NEVER carry your divisions past the decimal point! Decimal Number=97 Division Expression QuotientRemainder 97/2481

21. Covert Decimal to Binary Step 2 - For each subsequent row, take the quotient from the previous row and divide it by two Decimal Number=97 Division ExpressionQuotientRemainder 97/2481 48/2240 24/2120 12/260 6/230 3/211 1/201

22. Covert Decimal to Binary Step 3 – The remainder column only has ones or zeros. The last cell in the remainder column of the last row must be a "1". Read the 1s and 0s in the remainder column from the bottom to the top, we'll have our binary number!

23. Covert Decimal to Binary Decimal Number=97 Division Expression QuotientRemainderDirection 97/2481 48/2240 24/2120 12/260 6/230 3/211 1/201 Binary Number=1100001 Read

24. Whiteboard Examples In Class Correction 37 DEQR 37/2181 18/290 9/241 4/220 2/210 1/201 100101 2525 2424 23232 2121 2020 32*116*08*04*12*01*1 3200401 32+0+0+4+0+1= 37 Read

25. The last cell in the remainder column of the last row must be a "1“ because we need to use whole numbers (nonnegative integers). 1 ÷ 2 = 0 because 1 can not be divided into, 1 is the remainder. 37 (Odd Number) DEQR 37/2181 18/290 9/241 4/220 2/210 1/201 36 (Even Number DEQR 36/2180 18/290 9/241 4/220 2/210 1/201 Read

26. Hexadecimal Conversation and ASCII

27. Hexa + Decimal Base-16 number system It’s all Greek to me  “Sexa” = Latin = Six  “Decimal” = Latin = Ten  In 1963 IBM thought “Sexadecimal” was not politically correct  “Hexa” = Greek = Six  Since the western alphabet contains only ten digits, hexadecimal uses the letters A-F to represent the digits ten through fifteen.

28. Hexadecimal and Computing It is much easier to work with large numbers using hexadecimal values than decimal or binary.  One Hexadecimal digit = 4bits  Two hexadecimal digits = 8 bits  Eight bits=1 byte  This makes conversions between hexadecimal and binary very easy

29. Counting Hexadecimal Starting from zero, we count 00, 01, 02,03, 04, 05, 06, 07, 08, 09, 0A, 0B, 0C, 0D, 0E, 0F,10, 11, 12, 13, 14, 15, 16, 17 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, 22, 23, 24, 25,....

30. DecimalBinaryHexadecimal 000000 100011 200102 300113 401004 501015 601106 701117 810008 910019 101010a 111011b 121100c 131101d 141110e 151111f

31. Convert Hexadecimal to Decimal 11AA =108 16 3 16 2 16 1 16 0 4096*1256*116*108*1 40962561608 4096+256+160+8= 4520

32. Convert Decimal to Hexadecimal 4520 DEQR 4520/16282(.5*16)=8 282/1617(.625*16)=10 10=A 17/161(.0625*16)=1 1/160(.0625*16)=1 11A8 Quotient must be a whole number. If decimal, multiply decimal portion by 16 for remainder. Remainder must be a whole number. Read

33. Convert Hexadecimal to Binary Convert each hexadecimal digit into its 4-bit binary equivalent. equivalent 1AB Hex1AB Bin000110101011 000110101011

34. Convert Binary to Hexadecimal Converteach 4bit binary digit into its hexadecimal equivalent starting from the right. equivalent If there is an odd number of bits, add zeros to the left to make a complete 4bit digit. 110101011 Bin000110101011 Hex1AB 1AB

35. Uses  Web pages http://www.psyclops.com/tools/rgb/  Networking MAC address  Programming C, C++, C#, Java, Assembly  Geeky T-shirts DEADB4C0FFEE

36. ASCII American Standard Code for Information Interchange Each character is 7bits + 1bit for parity = 1byte Represents English characters as numbers, with each letter assigned a number from 0 to 127 This makes it possible to transfer data from one computer to another. Used to store text files http://www.pcguide.com/res/tablesASCII-c.html http://nickciske.com/tools/binary.php

37. Conversion Lab Section I: Converting from Decimal to Binary  1) 11  2) 27  3) 54  4) 113  5) 273 Section II: Converting from Binary to Decimal  6) 101  7) 1011  8) 10100  9) 111010  10) 1010001

38. Conversion Lab Section III: Convert Hexadecimal to Binary  11) 43B  12) DAB  13) 954  14) C0FFEE  15) B0A Section IV: Convert Binary to Hexadecimal  16) 11000001111  17) 10100011110  18) 100110  19) 11011110  20) 101110110001

39. Conversion Lab Section V: Convert Hexadecimal to Decimal  21) FF2  22) 45  23) 19D  24) 345  25) AA Section VI: Convert Decimal to Hexadecimal  26) 27  27) 85  28) 562  29) 4522  30) 5627