(or system of numeration) is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.
BINARY TO HEXADECIMAL
Example 1. Consider Binary: 1000100100110111 (a 16-bit Byte)
STEP 1 Break the Byte into 'quartets' - 1000 1001 0011 0111
STEP 2 Use the table above to covert each quartet to its Hex equivalent - 8937
Therefore ... 1000100100110111 = 8937Hex
Converting Decimal to Binary
Converting from Decimal to Binary is a little bit harder than going the other way. If you follow the steps you will have no problems.
To change from Decimal to Binary you carry out a series of subtractions based on the Binary 'Place' values...
|Binary Place Values |
|D7 |D6 |D5 |D4 |D3 |
|150 |
|ie Decimal 150 = Binary 10010110 |
You should check your answer by doing a Binary to Decimal conversion...
10010110 = 128 + 0 + 0 + 16 + 0 + 4 + 2 + 0 = 150
Octal to Binary
For some computers to accept octal data, the octal digits must be converted to binary. This process is the reverse of binary to octal conversion.
To convert a given octal number to binary, write out the octal number in the following format. We will convert octal 5678:
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Next, below each octal digit write the corresponding three-digit