Number system and its conversions
- 1. NUMBER SYSTEM SHILPA KRISHNA RESEARCH SCHOLAR
- 2. NUMBER SYSTEM DECIMAL BINARY OCTAL HEXADECIMAL
- 3. DECIMALNUMBER SYSTEM • The number system that we use in our day-to-life • In this number the base is 10.ie,total number of digits or symbols is ten. • Example: The value of the decimal number 4137 is calculated as - 4*1000 + 1*100 + 3*10 + 7*1 7000 100 30 7 Thousands Hundreds Tens Units Position position position position
- 4. BINARY NUMBER SYSTEM • Number system has two symbols 0(zero) and 1(one) called Binary Digits or bits. Its base is 2. • The weights assigned to bits in this system are powers of 2, namely 20 , 21 , 22 …… 1 0 1 0 1 Most Significant Bit Least Significant Bit
- 5. OCTALNUMBER SYSTEM • In this system there are only 8 digits ie. 0,1,2,3,4,5,6,7 • Its base is 8. Each position in an octal number represents a power of 8 ie, 80 , 81 , 82 …….
- 6. HEXADECIMALNUMBER SYSTEM • Number system has 16 digits. Base is 16 • In this system the first 10 digits are the digits of a decimal system 0,1,2,3,4,5,6,7,8,9 • The remaining six digits are denoted by A,B,C,D,E,F representing the decimal values 10,11,12,13,14,15 respectively
- 7. CONVERSION OF DECIMAL NUMBER TO BINARY • Find the binary equivalent of (23)10 2 23 2 11 1 LSB 2 5 1 2 2 1 2 1 0 0 1 MSB (23)10 = (10111)2
- 8. CONVERSION OF DECIMAL NUMBER TO OCTAL (3451)10 = ()8 ? 8 3451 8 438 3 LSB 8 54 6 8 6 6 0 6 MSB (3451)10 = (6663)8
- 9. CONVERSION OF DECIMAL NUMBER TO HEXADECIMAL (710)10 = ()16 ? 16 710 16 44 6 16 2 12 0 2 (710)10 = (2C6)16
- 10. CONVERSION OF BINARY NUMBER TO DECIMAL (1110101)2 = ()10 ? (1*26) + (1*25) + (1*24) + (0*23) + (1*22) + (0*21) + (1*20) 64 32 16 0 4 0 1 = 117 (1110101)2 = (117)10
- 11. CONVERSION OF BINARY NUMBER TO OCTAL SHORTCUT METHOD Example: (1101010)2 = ()8? 001 101 010 1 5 2 (1101010)2 = (152)8 OCTAL NUMBER BINARY EQUIVALENT 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111
- 12. CONVERSION OF BINARY NUMBER TO HEXADECIMAL SHORTCUT METHOD Example: (11010011)2 = 1101 0011 D 3 = (D3)16 DECIMAL HEXA DECIMAL BINARY 0 0 0000 1 1 0001 2 2 0010 3 3 0011 4 4 0100 5 5 0101 6 6 0110 7 7 0111 8 8 1000 9 9 1001 DECIMAL HEXA DECIMAL BINARY 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111
- 13. CONVERSION OF OCTAL NUMBER TO DECIMAL Example: (325)8 = ()10 ? (3*82) + (2*81) + (5*80) 3*64 + 2*8 + 5*1 192 + 16 + 5 = 213 (325)8 = (213)10
- 14. CONVERSION OF OCTAL NUMBER TO BINARY SHORTCUT METHOD (6751)8 = ( )2 ? 68 = 110 78 = 111 58 = 101 18 = 001 Hence (6751)8 = (110111101001)2
- 15. CONVERSION OF OCTAL NUMBER TO HEXADECIMAL (125)8 =( )16 ? Step 1 : convert octal number to decimal (1*82) + (2*81) + (5*80) 64 + 16 + 5 = 85 Step 2 : convert decimal number to hexadecimal 16 85 16 5 5 0 5 (125)8 = (55)16
- 16. CONVERSION OF HEXADECIMAL NUMBER TO DECIMAL (34F)16 = ( )10 ? (3*162) + (4*161) + (F*160) (3*256) + (4*16) + (15*1) 768 + 64 + 15 = 847 (34F)16 = (847)10
- 17. CONVERSION OF HEXADECIMAL NUMBER TO BINARY (ABC)16 = ( )2 ? A B C 1010 1011 1100 (ABC)16 = (101010111100)2
- 18. CONVERSION OF HEXADECIMAL NUMBER TO OCTAL (C1)16 = ( )8 ? (C*161) + (1*160) (12*16) + (1*1) 192 + 1 = 193 (decimal form) 8 193 8 24 1 8 3 0 0 3 (C1)16 = (301)8
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