Number System Conversion is tool for converting numbers between the various bases. In
this section, the number system conversion of binary, decimal and hexadecimal
number will be focus only. Repeated division is the most systematic
method to convert the number.
Binary Convertor
1) Convert binary number to
decimal number
Step:
I. Start with the last digit and multiply that digit with
20 .
II. Continue working from right to left multiply each
digit with an incremental increasing power of 2 (i.e. 21, 22, 23, 24, etc.).
III. Repeat
step 2 until all digits have been multiplied.
IV. Add the end
result of each worked power of 2 for a final answer.
Example:
a) 1110102
b) 110011.112
2)
Convert binary number to hexadecimal
Step:
I.
Break the Byte into ‘quartets’ from the right hand side.
II. Use
the table above to covert each quartet to its Hex equivalent.
Example:
a) 10001001001101112
b) 110011. 11 2
Decimal Convertor
1) Convert decimal number to
binary number
Step:
I. Divide the decimal number by 2.
II.
Write the remainder (which is either 0 or 1) at the right most position.
III.
Repeat the process of dividing by 2 until the quotient is 0 and
keep writing
the
remainder after each step of division.
IV.
Write the remainders in reverse order.
Example:
a) 1110
Conversions of Decimal Fractions to Binary Fractions
For
converting decimal fractions into binary fractions, we use multiplication.
Instead of looking for a remainder we look for an integer.
Step:
I.
Multiply the decimal fraction by 2
II.
If a non-zero integer is generated, record the non-zero integer otherwise record
0.
III.
Remove the non-zero integer and repeat the above steps till the fraction Value
becomes 0.
IV. Write
down the number according to the occurrence.
Example:
a)
0.312510
2) Convert decimal number to
hexadecimal number
We
divide by 16 instead of 2 or 8. If the remainder is in between 10 to 16, then
the number is represented by A to F respectively.
Example:
a)
4510
b)
0.7510
Hexadecimal convertor
1)
Convert hexadecimal number to binary number
Step:
I. Convert each hexadecimal digit to its 4-bit binary
equivalent.
II.
Combine all the binary numbers.
Example:
a)
2D16
b) 2D.C16
2) Convert hexadecimal number to
decimal number
We do the conversion of hexadecimal fractions to decimal fractions
in the similar manner as we have done the conversion of binary fractions to
decimal fractions. Here weight of bit is 16-1, 16-2…….
Example:
a)
2D16
b)
2D.C16
This is dummy text. It is not meant to be read. Accordingly, it is difficult to figure out when to end it. But then, this is dummy text. It is not meant to be read. Period.
ConversionConversion EmoticonEmoticon