 | Binary-To-Decimal Conversion |
| | Any binary number can be converted to its decimal equivalent simply by summing together the weights of the various positions in the binary number which contain a 1. |
| | | Binary | Decimal | | 110112 |
| | 24+23+01+21+20 | =16+8+0+2+1 | | Result | 2710 | |
| | and |
| | | Binary | Decimal | | 101101012 |
| | 27+06+25+24+03+22+01+20 | =128+0+32+16+0+4+0+1 | | Result | 18110 | |
| | You should have noticed that the method is to find the weights (i.e., powers of 2) for each bit position that contains a 1, and then to add them up. |
| | Decimal-To-Binary Conversion |
| | There are 2 methods: |
| | - Reverse of Binary-To-Decimal Method
- Repeat Division
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 | Reverse of Binary-To-Decimal Method |
| | | Decimal | Binary | | 4510 | =32 + 0 + 8 + 4 +0 + 1 | |
| =25+0+23+22+0+20 | | Result | =1011012 | |
| | Repeat Division-Convert decimal to binary |
| | This method uses repeated division by 2. |
| | Convert 2510 to binary |
| | | Division | Remainder | Binary | | 25/2 | = 12+ remainder of 1 | 1 (Least Significant Bit) | | 12/2 | = 6 + remainder of 0 | 0 | | 6/2 | = 3 + remainder of 0 | 0 | | 3/2 | = 1 + remainder of 1 | 1 | | 1/2 | = 0 + remainder of 1 | 1 (Most Significant Bit) | | Result | 2510 | = 110012 | |
| | The Flow chart for repeated-division method is as follows: |
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| | Binary-To-Octal / Octal-To-Binary Conversion |
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| | | Octal Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | | Binary Equivalent | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111 | |
| | Each Octal digit is represented by three binary digits. |
| | Example: |
| | 100 111 0102 = (100) (111) (010)2 = 4 7 28 |
| | Repeat Division-Convert decimal to octal |
| | This method uses repeated division by 8. |
| | Example: Convert 17710 to octal and binary |
| | | Division | Result | Binary | | 177/8 | = 22+ remainder of 1 | 1 (Least Significant Bit) | | 22/ 8 | = 2 + remainder of 6 | 6 | | 2 / 8 | = 0 + remainder of 2 | 2 (Most Significant Bit) | | Result | 17710 | = 2618 | | Binary | | = 0101100012 | |
| | Hexadecimal to Decimal/Decimal to Hexadecimal Conversion |
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| | Example: |
| | 2AF16 = 2 x (162) + 10 x (161) + 15 x (160) = 68710 |
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| | Repeat Division- Convert decimal to hexadecimal |
| | This method uses repeated division by 16. |
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| | Example: convert 37810 to hexadecimal and binary: |
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| | | Division | Result | Hexadecimal | | 378/16 | = 23+ remainder of 10 | A (Least Significant Bit)23 | | 23/16 | = 1 + remainder of 7 | 7 | | 1/16 | = 0 + remainder of 1 | 1 (Most Significant Bit) | | Result | 37810 | = 17A16 | | Binary |
| = 0001 0111 10102 | |
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| | Binary-To-Hexadecimal /Hexadecimal-To-Binary Conversion |
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| | | Hexadecimal Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | | Binary Equivalent | 0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | |
| | | Hexadecimal Digit | 8 | 9 | A | B | C | D | E | F | | Binary Equivalent | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 | |
| | Each Hexadecimal digit is represented by four bits of binary digit. |
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| | Example: |
| | 1011 0010 11112 = (1011) (0010) (1111)2 = B 2 F16 |
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| | Octal-To-Hexadecimal Hexadecimal-To-Octal Conversion |
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| | - Convert Octal (Hexadecimal) to Binary first.
- Regroup the binary number by three bits per group starting from LSB if Octal is required.
- Regroup the binary number by four bits per group starting from LSB if Hexadecimal is required.
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| | Example: |
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| | Convert 5A816 to Octal. |
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| | | Hexadecimal | Binary/Octal | | 5A816 | = 0101 1010 1000 (Binary) | |
| = 010 110 101 000 (Binary) | | Result | = 2 6 5 0 (Octal) | |
