Salisbury

Numbers we use in Auto Shop

Why do I need to know this. When working on the computers in the auto shop sometimes we need to look into the back door to find out what the computer is thinking. We call this mode 6. Many times the numbers we see are Hexadecimal. I feel that you also need to understand the Binary system because that is how the computers talk. It is easier for the computer to go from binary to Hexadecimal then to decimal. So that is why it is displayed that way.

Base ten or Decimal This is the basic numbering system we use. We call it Base ten because we use ten distinct values (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9) to represent any numbers, no matter how large.

Base ten or Decimal I hope we have used this enough that we really understand it. If we take the number 10 3 we have 10 x 10 x 10 = 1,000 Ten Million Hundred Thousand Ten Thousand Hundredsten ,000,0001,000,000100,00010,0001,

Binary or Base 2 This is the one that computers use (0,1) because the computer is either on or off. What I mean is that the computer can either say Yes, a positive answer or No a negative answer. ON or OFF

Binary or Base

Hexadecimal or Base 16 This is used in digital computing to represent bytes. Base 16 because it uses the 16 symbols to represent the values (0- 9 but then for ten thru fifteen we use the letters A, B, C, D, E, F.) A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Hexadecimal or Base 16 The last digit on the right is the ones 16 x 0 = 0 so anything in this spot will be a number less then 16. Each position will add a value 16 times greater then the last position. F = _____ in decimal? A = _____ in decimal?

Hexadecimal or Base 16 The second digit, think of it as a box with 16 numbers in it 16 x 1 = 16. For example if the number is 50 you would take 5 x 16 = 80, the 0 is just that = _____ in decimal? 9A = _____ in decimal?

Hexadecimal or Base = _____ in decimal? 4 x 16 = 64 3 = 3 Total = 67 9A = _____ in decimal? 9 x 16 = 144 A = 10 Total = 154

Hexadecimal or Base 16 The Third digit will add a value 16 times greater so if the number is 4 you would take 4 x 16 x 16 = 1024 (1024 divided by 4 = 256 Where did that number come from, a box of 256) 568 = _____ in decimal?

Hexadecimal or Base = _____ in decimal? 5 x 16 x 16 = x 16 = 96 8 = 8 Total =

Hexadecimal or Base 16 The fourth digit would continue to add a value 16 times greater 1 x 16 x 16 x 16 = 4096 (A box of 4096) D46F = _____ in decimal?

Hexadecimal or Base 16 Do not look at the answer, do your work!! D46F = _____ in decimal?

Hexadecimal or Base 16 D46F = _____ in decimal? D x 16 x 16 x 16 = x 16 x 16 = x 16 = 96 F = 15 Total =

Base ten or DecimalBase 16 or HexadecimalBase 2 or Binary A B C D E F1111 A Basic conversion chart between the three numeral systems.

Hexadecimal Multiplication Table Courtesy of Bernard Ladenthin At wikipedia.org

Calculator’s Most of the time we just use the normal calculator that comes on the computer. But if you go to View and change it to Scientific we can have more functions at our hands.

Calculator’s Notice that when we put it into scientific that it automatically goes to Dec (Decimal) That is what we use the most.

Calculator’s We can change our answers very easy by just clicking on the numeral system we want to convert it to.

Calculator’s When in Binary, notice that the only digits are 0,1.

Calculator’s Look what happens when we switch to Hex.

Calculator’s

Notice that the letters A, B, C, D, E, F are now usable.

Changing from Decimal to Hexadecimal to Binary The easy way to change from one numbering system to another is just click on the system you want.

Start with Decimal

Click on Hex (Hexadecimal)

Click on Bin (Binary)