By..Ms.Patsara Aroonmeesri

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

2. Alternative names for some of the numbers are base 2 = binarybase 3 = ternary base 4 = quarternary base 5 = quinary(hand) base 6 = senary base 7 = septenary

3. base 8 = octal base 9 = nonary base 10 = decimal (denary) base 11 = undecimal base 12 = duodecimal(dozenal) base 13 = tredecimalbase 16 = hexadecimal

4. The binary numeral system ( base-2 number system ) There are two symbols, 0 and 1 instead of the base-2 number system. And write 2 in the bottom ofa number. Such as 1012 , 112 , 110012

5. 1 1 0 1 0 1 x x x x x x Whole number places and place values of the binary numeral system. 22 23 24 25 21 20 1101012= (1 x 25) + (1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 1)

6. x ( ) ( ) 1 ( ) ( ) x 0 x ( ) ( ) 1 20 21 22 + + + + Converting binary to decimal To convert binary into decimal is very simple and can be done as shown below: Convert 1012todecimal. Example I 1012= = 0x2 1x4 1x1 = 4 + 0 + 1 = 5 Ans.

7. x x 23 22 x 20 ( ) + ( ) + ( ) + ( ) x 21 ( ) + ( ) ( ) 1 ( ) + 1 0 1 + Convert 10112 todecimal. Example II 10112= = 1x8 0 1x2 1x1 = 8 + 0 + 2 + 1 Ans. = 11

8. Exercise Convert the following binary numbers to decimal numbers. 6.) 1002 1.) 102 7.) 1102 2.) 112 3.) 10012 8.) 100112 4.) 11002 9.) 101012 10.) 1010112 5.) 1112

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

10. Convert 6 to binary. Example I 2 6 3 Remainder0 2 Remainder1 1 Ans. Thus6= 1102

11. Convert 11 to binary. Example II 11 2 Remainder1 5 2 2 R1 2 R0 1 Ans. Thus11= 10112

12. Exercise Convert the following decimal numbers to binary numbers. 6.) 19 1.) 4 2.) 7 7.) 20 3.) 10 8.) 33 4.) 11 9.) 42 10.) 55 5.) 16

13. Bye Bye Thanks for learning.