By..Ms.Patsara Aroonmeesri

1. Base Numeral For M.1 By..Ms.Patsara Aroonmeesri Kumphawapi School

2. The symbols of the numeral system. Base 3 number system There are 3 symbols 0,1,2. Base 5 number system There are 5 symbols 0,1,2,3,4. Base 6 number system There are 6 symbols 0,1,2,3,4,5. Base 8 number system There are 8 symbols 0,1,2,3,4,5,6,7. Base 9 number system There are 9 symbols 0,1,2,3,4,5,6,7,8. Base 11 number system There are 11 symbols 0,1,2,3,4,5,6,7,8,9,A. Base 12 number system There are 12 symbols 0,1,2,3,4,5,6,7,8,9,A,B. ( A = 10 และ B = 11 )

4. The numeral system We write the number (another base) in the bottom of the number. Such as.. 1123 201135 10056 1068 10879 1A0111 5AB12

5. x ( ) ( ) 1 ( ) ( ) x 1 x ( ) ( ) 2 30 31 32 + + + + Converting another base to decimal To convert another base into decimal is the same as to convert binary into decimal. Example I Convert 1123todecimal. 1123= = 1x3 1x9 2x1 = 9 + 3 + 2 = 14 Ans.

6. x x 63 62 x 60 ( ) + ( ) + ( ) + ( ) x 61 ( ) + ( ) ( ) 0 ( ) + 1 0 5 + Convert 10056 todecimal. Example II 10056= = 1x216 0 0 5x1 = 216 + 0 + 0 + 5 Ans. = 221

7. Exercise Convert the following each base numbers to decimal numbers. 6.) 10718 1.) 1013 7.) 1819 2.) 12014 3.) 10215 8.) 19A11 4.) 12416 9.) 101012 10.) AB012 5.) 10017

8. Converting decimal to another base number 1.Divide the decimal value by the number of another base number. 2.Then write down the remainder. 3.Repeat 1,2 4.Until you cannot divide by each number anymore. 5.Stop divide by each number. 6.These remainders tell you what the base number is. 7.Write the remainders from bottom to the top , that is the another base number.

9. Convert 12 to base 3. Example I 3 12 4 Remainder0 3 1 Remainder1 Ans. Thus12= 1103

10. Convert 2542 to base 11 Example II 2542 11 Remainder1 231 11 R0 21 11 R10 (A) 1 Ans. Thus2542= 1A0111

11. Bye Bye Thanks for learning.