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# Number system

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### Number system

1. 1.  Non-Positional Number System  Positional Number System
2. 2.  Difficult to perform arithmetic operation.  For example:- I, II, III, IV, V, VI, VII, VIII, IX, X.
3. 3.  The values of each digit is determined by:-  -Digit itself  -Position of the digit  -Base of the number system
4. 4.  The base is equal to 10.  Uses 10 different symbols.
5. 5.  The base is 2.  Each position represents a power of the base 2.  For example:- Conversion from 00111101 to decimal is-  128 64 32 16 8 4 2 1  0 0 1 1 1 1 0 1 =(0*128) + (0*64) + (1*32) + (1*16) + (1*8) + (1*4) + (0*2) + (1*1) = 32 + 16 + 8 + 4 + 1 =(61)10
6. 6.  The base is 8.  Largest single digit is 7.
7. 7.  The base is 16.  Combination of 0-9 and A-F.
8. 8. Decimal Binary Hexadecimal Decimal Binary Hexadecimal 1 1 1 9 1001 9 2 10 2 10 1010 A 3 11 3 11 1011 B 4 100 4 12 1100 C 5 101 5 13 1101 D 6 110 6 14 1110 E 7 111 7 15 1111 F 8 1000 8
9. 9.  Convert each octal digit to 3-bit binary form.  Combine all the 3 bits binary form.  Divide the binary numbers into the 4-bit binary form.  Convert these 4 bits blocks into their respective hexadecimal symbols .
10. 10. Example: Octal number is 2327 Octal Number 2 3 2 7 Binary Coded value 010 011 010 111 combining 3-bit blocks we have 010011010111 Dividing of binary numbers into 4-bit binary blocks and converting these blocks into their respective symbols, we have 0100 1101 0111 4 D 7
11. 11. Same procedure to convert decimal number to binary, octal & hexadecimal. Same procedure to convert from binary, octal & hexadecimal to decimal numbers .