1. NUMBER SYSTEM

2. Number System Number Base B => B symbols
Base 16(Hexa):0, 1,……9, A ,…, E, F
Base 10 (Decimal): 0, 1, 2,……, 7, 8, 9
Base 8(Octal): 0, 1, 2, 3, 4, 5, 6, 7
Base 2 (Binary): 0, 1

3. Number System (cont) Number representation:
d31d d2d1d0 is a 32 digit number
value = d31x B31 + d30 x B d2 x B2 + d1 x B1 + d0 x B0

4. Decimal Numbers: Base 10 Base or Radix is 10
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Example:
41210 = 4x x x100
= = 412

5. Binary Numbers: Base 2 Base or Radix is 2 Digits: 0, 1 Example:
1012 = 1x22 + 0x21 + 1x20
= = 5

6. Octal Numbers: Base 8 Base or Radix is 8
Digits: 0, 1, 2, 3, 4, 5, 6, 7
Example:
1238 = 1x82 + 2x81 + 3x80 =
= 83

7. Hexadecimal Numbers: Base 16
Digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F:
A  10
B  11
C  12
D  13
E  14
F  15
Example:
1216 = 1x x160
= 16 +2
= 18

8. Conversions Decimal to Base N Base N to Decimal
Successive Division by N
(Remainder Method)
Multiplication with power of N

9. Decimal to Binary

10. Conversion of 2510 to Binary
2 25
1 - 1
2510=110012

11. Binary to decimal conversion
11001
1X20 = 1
0X21 = 0
0X22 = 0
1X23 = 8
1X24 = 16
2510

12. Decimal to Octal

13. Conversion of to Octal
8 125
12510=1758

14. Octal to decimal conversion
175
5X80 = 5
7X81 = 56
1X82 = 64
125
1758 = 12510

15. Conversion of 8410 to Octal
8 84
8410=1248

16. Octal to decimal conversion
124
4X80 = 4
2X81 = 16
1X82 = 64 84
1248 = 8410

17. Decimal to Hexa

18. Conversion of 45010 to Hexadecimal
16 450
45010=1C216

19. Hexa to decimal conversion
450
1C216 = 45010

20. Conversion of 38510 to Hexadecimal
16 385
38510=18116

21. Hexa to decimal conversion
181
1X160 =
8X161 = 128
1X162 = 256
385
18116 =

22. Other Conversions
BINARYOCTAL
BINARYHEXA
OCTALHEXA etc,.

23. BINARYOCTAL
OCTAL – BASE 8 = 23
3 DIGIT BINARY NUMBER
Example:  OCTAL
110012=318

24. Example:  OCTAL
=1638

25. BINARYHEXA
HEXA – BASE 16 = 24
4 DIGIT BINARY NUMBER
Example:  HEXA
110012=1916

26. Example:  OCTAL
=1638

27. OCTALHEXA
OCTALBINARYHEXA
Example:318  HEXA
318=1916

28. HEXA  OCTAL
Example: 1BD  OCTAL
B D
1BD = 6758

29. Conversion of 25.12510 to Binary
2 25
1 - 1
2510=110012

30. 0.125 X 2 = 0.250
0.250 X 2 = 0.5
0.5 X 2 = 1.0 =

31. Binary to decimal conversion
1X2-3 =
0X2-2 = 0
0X2-1 = 0
1X20 = 1
0X21 = 0
0X22 = 0
1X23 = 8
1X24 = 16

32. Conversion of to Octal
8 84
8410=1248

33. 0.250 X 8 = 2.000 =

34. Octal to decimal conversion
124.2
2X8-1 =
4X80 = 1
2X81 = 0
1X82 = 0

35. ASSIGNMENT

36. DECIMAL TO BINARY 43 79
107
241
476

37. DECIMAL TO OCTAL 39
152
284
758
2534

38. DECIMAL TO HEXA 75
826
3128
7359
4756

39. DECIMAL TO OTHER
63 BASE4
279 BASE6
161 BASE7

40. BINARY  OCTAL,HEXA

41. OCTAL  HEXA
473
1235
724
5774
4625

42. BASE2
OCTAL
HEXA