The Plea of an Aborted Fetus

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  • Topic: Binary numeral system, Octal, Hexadecimal
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  • Published : December 1, 2010
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NUMBER SYSTEM
(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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