Any other numbering system to decimal.docx
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The document provides a comprehensive guide on converting different numbering systems (binary, octal, and hexadecimal) to decimal. It includes detailed examples showing the conversion process for both integer and fractional parts, illustrating how to use place values for calculations. The document also presents specific conversions with calculations to demonstrate practical applications.
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Any other numbering system to decimal.docx
- 1. NUMBER SYSTEM CONVERSION Dr.S.ANITHA Any other numbering system to Decimal I. Binary ∑ digit * 2pv II.Octal ∑ digit * 8pv III.Hexadecimal ∑ digit * 16pv Note: Pv – place value +ve place values (for integer part) 0,1,2,.. -ve place values (for fractional part) -1,-2,.. I.Binary to Decimal (11011)2 = (?)10 1 1 0 1 1 X X X X X 24 + 23 + 22 + 21 + 20 16 8 4 2 1 16 + 8 + 0 + 2 + 1 = 27
- 2. (11011)2 = (27)10 Fractional part (11011.10)2 = (?)10 1 1 0 1 1 1 0 X X X X X X X 24 + 23 + 22 + 21 + 20 2-1 2-2 16 8 4 2 1 0.5 0.25 16 + 8 + 0 + 2 + 1+ 0.5+ 0 = 27.5 (11011.10)2 = (27.5)10 ********************************************* (101110.11)2 = ? 46.75
- 3. II.Octal to Decimal (761)8 = ()10 7 6 1 X X X 82 + 81 + 80 + 64 8 1 448 + 48 + 1 = 497 (761)8 = (497)10
- 4. Fractional part (761.53)8 = ()10 7 6 1 5 3 X X X X X 82 + 81 + 80 + 8-1 + 8-2 + 64 8 1 .125 .015625 448 + 48 + 1 + .625 + .046875 = 497.671875 (652.12)8 = (?)10 = 426.15625 ****
- 5. III. Hexadecimal to Decimal (761)16 = ()10 7 6 1 X X X 162 + 161 + 160 + 256 16 1 1792 + 96 + 1 = 1889 (761)16 = (1889)10 (AC5)16 = ()10 = 2757
- 6. Fractional part (761.53)16 = ()10 7 6 1 5 3 X X X X X 162 + 161 + 160 + 16-1 + 16-2 + 256 16 1 .0625 .00390625 1792 + 96 + 1 + .3125 + .01171875 = 1889.32421875 ***** (652.12)16 = (?)10 = 1618.0703125 *****
- 7. (1CA)16 = (?)10 1 12 10 X X X 162 + 161 + 160 + 256 16 1 256 + 192 + 10 = 458 ****