alll About Number Systems, learning of Conversion of ... Binary NS to Decimal NS, Octal NS, Hexa-Decimal NS ... Decimal NS to Binary NS, Octal NS, Hexa-Decimal NS ... Octal NS to Binary NS, Decimal NS, Hexa-Decimal NS ... Hexa-Decimal NS to Binary NS, Decimal NS, Octal NS

1. What are Number Systems?
• Number systems are the technique to represent numbers in the computer system
architecture, every value that you are saving into or getting from computer memory
has a defined number system. Computer architecture supports following number
systems.
• Binary Number System (2 digits)
• Octal Number System (8 digits)
• Decimal Number System (10 digits )
• Hexa-decimal Number System (16 digits)

2. NUMBER SYSTEMS

3. Conversion Among Bases:
Hexadecimal
Decimal Octal
Binary
• The possibilities

4. Decimal Binary Octal
Hexa-
Decimal
0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 7 7
8 1000 10 8
9 1001 11 9
Decimal Binary Octal
Hexa-
Decimal
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F

5. Binary Number System
• Digital computers represents all kinds of data and information in the binary system.
• Binary Number System consists of two digits 0 and 1. Its base is 2. Each digit or bit
in binary number system can be 0 or 1.
• Binary to Decimal Conversion Techniques:
• Multiply each bit by 2n, where n is the “weight” of the bit.
• The weight is the position of the bit, starting from 0 on the right.
• Add the results.
• Example 1010112 = 4310

6. Binary Number System
• Binary to Octal Conversion Techniques:
• Group binary digits in a 3 bits, starting on right side.
• Convert to octal digits.
• Example 10110101112 = 13278
• Binary to Hexa-decimal Conversion Techniques:
• Group binary digits in a 4 bits, starting on right side.
• Convert to hexa-decimal digits.
• Example 10101110112 = 2BB16

7. Binary to Decimal Conversion
•

8. Binary to Octal Conversion
•

9. Binary to Hexa-decimal Conversion
•

10. Octal Number System
• Octal number system is the base 8 number system and uses the digits from 0 to 7.
This number system provides shortcut method to represent long binary numbers
• The number after 7 is 10. the number after 17 is 20 and so forth.
• Octal to Decimal Conversion Techniques:
• Multiply each bit by 8n, where n is the “weight” of the bit.
• The weight is the position of the bit, starting from 0 on the right.
• Add the results.
• Example 7248 = 46810

11. Octal Number System
• Octal to Binary Conversion Techniques:
• Convert octal digit in a 3 bits, starting on the right side.
• Example 7058 = 1110001012
• Octal to Hexa-decimal Conversion Techniques:
• Use binary as an intermediary
• Example 10768 = 23E16

12. Octal to Decimal Conversion
•

13. Octal to Binary Conversion
•

14. Octal to Hexa-decimal Conversion
•

15. Decimal Number System
• Decimal number system is the base 10 number system and uses the digits from 0 to
9. Using these digits you can express any quantity.
• It is what we most commonly use.
• Decimal to Binary Conversion Techniques:
• Divide each bit by 2, keep track of the remainder
• First remainder is bit 0 (LSB, least-significant bit)
• Example 12510 = 11111012

16. Decimal Number System
• Decimal to Octal Conversion Techniques:
• Divide each bit by 8, keep track of the remainder
• First remainder is bit 0 (LSB, least-significant bit)
• Example 123410 = 23228
• Decimal to Hexa-decimal Conversion Techniques:
• Divide each bit by 16, keep track of the remainder
• First remainder is bit 0 (LSB, least-significant bit)
• Example 123410 = 4D216

17. Decimal to Binary Conversion
• 125 = 2 125 --- 1
2 62 --- 0
2 31 --- 1
2 15 --- 1
2 7 --- 1
2 3 --- 1
1
= 11111012

18. Decimal to Octal Conversion
• 1234 =
8 1234 --- 2
8 154 --- 2
8 19 --- 3
8 2
= 23228

19. Decimal to Hexa-decimal Conversion
• 1234 =
16 1234 --- 2
16 77 --- 13
16 4
= 4 13 2
= 4D216

20. Hexa-decimal Number System
• Hexa-decimal number system is the base 16 and uses the digits from 0 to 9 and A to
F. This number system provides shortcut method to represent long binary numbers.
• Unlike binary and octal, hexa-decimal has six additional symbols that it uses beyond
the conventional ones found in decimal.
• Hexa-decimal to Decimal Conversion Techniques:
• Multiply each bit by 16n, where n is the “weight” of the bit.
• The weight is the position of the bit, starting from 0 on the right.
• Add the results.
• Example ABC16 = 274810

21. Hexa-decimal Number System
• Hexa-decimal to Binary Conversion Techniques:
• Convert hexa-decimal digit in a 4 bits, starting on the right side.
• Example 10AF16 = 00010000101011112
• Hexa-decimal to Octal Conversion Techniques:
• Use binary as an intermediary
• Example 1F0C16 = 00011111000011008

22. Hexa-decimal to Decimal Conversion
•

23. Hexa-decimal to Binary Conversion
•

24. Hexa-decimal to Octal Conversion
•

25. End