number system
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Types of Number System
Non-Positional Number System Positional Number System
Non-Positional Number System
Difficult to perform arithmetic operation. For example:- I, II, III, IV, V, VI, VII, VIII, IX, X.
Positional Number System The values of each digit is determined by:- -Digit itself -Position of the digit -Base of the number system
Decimal Number The base is equal to 10. Uses 10 different symbols.
Binary Number System 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
Octal Number System The base is 8. Largest single digit is 7.
Hexadecimal Number System The base is 16. Combination of 0-9 and A-F.
Decimal, Hexadecimal and Binary representations
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
Conversion of decimal representation to Binary
Conversion of Binary representation to decimal
Conversion of Hexadecimal to binary
Conversion of binary to hexadecimal
Conversion of decimal representation to hexadecimal
Conversion of hexadecimal representation to decimal
Conversion of octal representation to hexadecimal 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 .
Continue…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
Conclusion Same procedure to convert decimal number to binary, octal & hexadecimal.Same procedure to convert from binary, octal & hexadecimal to decimal numbers .
