Objective 1.02 Understand Numbering Systems

Transcription

1 Objective.0 Understand Numbering Systems C O M P U T E R P R O G R A M M I N G I Number Systems Number systems we will talk about: Decimal (Base 0 ) Binary (Base ) Hexadecimal (Base 6 )

2 Decimal The number system we use in math and in life. 3 Base 0: ten one digit numbers: 0,,,3,,5,6,7,, After 9 comes 0 (the first two digit number) of course. 0 = 00 Base squared = 00 Decimal What can we say about the decimal system? It is our day to day number system The Decimal system has 0 digits; values are from 0 to

3 Binary 5 Binary is Base one digit numbers 0 and For example: Base 0 of = Binary 000 or 00 0 =00 works in binary too! squared = Machine Language Binary or Base : Only contains types of digits; or 0. The power of. Each digit from the right to the left is increased by power of. Each one () digit has a value representing on and each zero (0) digit do not hold a value representing off. OOOO OOOO Ex: = The right most digit () = ( 0 ) The two middle digits are 0 therefore have no value. The left most digit () = ( 3 or xx). The other digits have no value. The total value of all numbers would = 9. (+0+0+) ex: = 5 in decimal amount =

4 Why Binary? Computers operate on a series on electric impulses. 7 If the current is flowing the circuit is complete (), otherwise the current is off (0) Write down the powers of from Powers of Remember from math the powers of :,,,, 6, 3, 6, (first ) Remember any number to the zero power is and any number to the power is that number. So if Decimal = 00 in binary, what does decimal 5 equal in binary?

5 Powers of Remember from math the powers of : 9,,,, 6, 3, 6, (first ) Remember any number to the zero power is and any number of the power is that number. So if Decimal = 00 in binary, what does decimal 5 equal in binary? 0 A: 0 0 The s So let s go beyond our basic example. Remember the most right digit has the least significant value and the most left digit has the most significant value. What is in Decimal? That would be 55. So would be 56, right?

6 Let s Try This On your paper draw columns Above each column label a power of, starting at in the first (left most) column. Finish with in the last (right most) column Example Binary Figure out the following numbers in binary Decimal

7 Example Binary Answers Figure out the following numbers in binary: Dec Binary (Answer) Hexadecimal Hex is Base 6 There are fifteen one digit numbers: 0,,,3,,5,6,7,,9,A,B,C,D,E,F What comes after F? Remember our rule: 0 =00 (6 =56 in decimal) This works in Hex as it does for ANY number system. 7

8 Hexadecimal 5 Contains 6 digits starting with 0-9 & A-F containing the values from 0 5. Hex Dec Hex Dec -Hex 0-F and so on 0 = 0 0 = 6 -Each digit carries a value of 6. = = 7 -Hex = 6 + Decimal = 0 (Hexadecimal =6) = = -Hexadecimal is only bits (binary value) 3 = 3 3 = 9 -ex: = 5 in decimal F in Hex value = = 0 -Another ex: = 9C in Hex and 5 = 5 5 = -56 in Decimal value. 6 = 6 6 = 7 = 7 7 = 3 = = 9 = 9 9 = 5 Remember! Hex is only bits long and its A = 0 A = 6 highest value is F in Hex or B = B = 7 5 in decimal or in binary. C = C = D = 3 D = 9 Mainframe computers use Hexadecimal to E = E = 30 utilize less disk space. F = 5 F = 3 Hexadecimal Conversion 6 Hex 9F to binary 9 F F Base 6 = 00 Base Hex 9F to Decimal 9 F F Base 6 = 59 Base 0 (6 * 9) + ( * 5) = 59 in Decimal Add the values

9 Hexadecimal Think if you had 3 hands. You would have 5 fingers right? That is what hex has! So after 9 comes A (0), B (), C (), D (3), E () and F (5) Let try our example again in Hex. 7 Another Conversion to Hexadecimal Figure out the following Decimal numbers to Hex: Decimal Ask How many of 56 can come out of 56 (our decimal number)? 0. Ask How many of 6 can come out of 56? 3 (3 * 6 = with left over) Put the 3 in the 6 s spot 3. Ask How many of can come out of (the left over)? with 0 left over 9

10 Example Hex Answers Figure out the following Decimal numbers to Hex: Dec Hex C Conclusion 0 In this lesson we learned about number systems used in Programming. Decimal Binary Hexadecimal 0

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