(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: [pic]

Next, below each octal digit write the corresponding three-digit binary-coded octal equivalent: [pic]

Solution: 5678 equals 101 110 1112

Remove the conversion from the format:

1011101112

As you gain experience, it may not be necessary to use the block format. An octal fraction (.1238) is converted in the same manner, as shown below: [pic]

Solution: .1238 equals .0010100112

Apply these principles to convert mixed numbers as well.

Convert 32.258 to binary:

[pic]

Solution: 32.258 equals 011010.0101012

Binary Number into Octal

First of all, we enter the Binary Number value and performing the calculation we get its equivalent Octal number value.

Few Examples are shown below,

Binary to Octal Conversions

1010010 is converted into 122

1000100101 is converted into 1045

Other Binary to Octal number conversions can be carried out in the similar manner.

Hex Number into Octal

First of all, we enter the Hex Number value and performing the calculation we get its equivalent Octal number value.

Few Examples are shown below,

Hex to Octal Conversions

1BE is converted into 676

31 is converted into 61

BCD is converted into 5555

Other Hex to Octal number conversions can be carried out in the similar manner.

Octal Number into Decimal

First of all, we enter the Octal Number value and performing the calculation we get its equivalent Decimal number value.

Few Examples are shown below,

Octal to Decimal Conversions

676 is converted into 446

61 is converted into 49

1000 is converted into 512

Other Octal to Decimal number conversions can be carried out in the similar manner.

Octal Number into Hex

First of all, we enter the Octal Number value and performing the calculation we get its equivalent Hex number value.

Few Examples are shown below,

Octal to Hex Conversions

676 is converted into 1BE

61 is converted into 31

5555 is converted into B6D

Other Ocal to Hex number conversions can be carried out in the similar manner.

Convert Decimal to Octal

First of all, we enter the...

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