Conversion methods
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This document discusses different number conversion methods between denary, binary, hexadecimal, and octal number systems. It provides tables that show how to convert between the number systems by grouping bits or dividing and taking remainders at each step. Conversion methods covered include binary to hexadecimal, binary to decimal, hexadecimal to decimal, decimal to hexadecimal, decimal to binary, and decimal to octal.
Conversion methods
- 2. Denary Binary Hexadecimal Octal 0 00000000 0 0 1 00000001 1 1 2 00000010 2 2 3 00000011 3 3 4 00000100 4 4 5 00000101 5 5 6 00000110 6 6 7 00000111 7 7 8 00001000 8 9 00001001 9 10 00001010 A 11 00001011 B 12 00001100 C 13 00001101 D 14 00001110 E 15 00001111 F 2
- 3. Hexadecimal numbers Hexadecimal uses the digits 0-9 and the letters A-F, so counting would look like this: 0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 21 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 30 31 32 32 … etc 3
- 4. Binary to Hexadecimal 1. Draw the table a. eg 10110001 add it to your table b. Divide it into groups of 4 bits starting from the right hand side c. In each group start 23 22 21 20 d. Add up the values in each group and from the heaxadecimal table replace the value 23 22 21 20 23 22 21 20 1 0 1 1 0 0 0 1 8 + 0 + 2 + 1 = 11 0 + 0 + 0 + 1 = 1 B 1 4
- 5. Binary to Decimal (Denary) 1. Draw the table a. eg 10010001 add it to your table b. Add all the values in the second row that have a 1 in the third row c. 128+16+1 = 145 27 26 25 24 23 22 21 20 128 64 32 16 8 4 2 1 1 0 0 1 0 0 0 1 5
- 6. Hexadecimal to Decimal • Eg. B1 (2 characters) • Draw the table 162 161 160 256 16 1 B 1 Decimal value 11 1 11x16 =176 1x1 =1 176 + 1 = 177 Decimal to hexadecimal from table slide 2 Multiply these values eg 11x16 and 1x1 then add the results 6
- 7. Decimal to hexadecimal • Eg 255 • Divide by 16 • 255/16 = 15 and a remainder of 15 • 15/16 = 0 and a remainder of 15 decimal 15 15 hexadecimal F F Result = FF Most significant Least significant 7
- 8. Decimal to hexadecimal eg 325 325/16 = 20 and a remainder of 5 20/16 =1 and a remainder of 4 1/16 = 0 and a remainder of 1 32510 1 4 5 Result = 14516 or 0x145 Most significant Least significant 8
- 9. Decimal to Binary Draw the table Eg 325 29 28 27 26 25 24 23 22 21 20 512 256 128 64 32 16 8 4 2 1 1 0 1 0 0 0 1 0 1 OR 9
- 10. Decimal to Binary Eg 324 324/2 = 162 and a remainder of 0 162/2 = 81 and a remainder of 0 81/2 = 40 and a remainder of 1 40/2 = 20 and a remainder of 0 20/2 = 10 and a remainder of 0 10/2 = 5 and a remainder of 0 5/2 = 2 and a remainder of 1 2/2 =1 and a remainder of 0 1/2 = 0 and a remainder of 1 The result is 101000100 Most significant Least significant 10