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NUMBER SYSTEM CONVERSION
There are many methods or techniques which can be used to convert numbers from one base to another. We'll demonstrate here the following โ
Decimal to Other Base System
Other Base System to Decimal
Other Base System to Non-Decimal
Shortcut method โ Binary to Octal
Shortcut method โ Octal to Binary
Shortcut method โ Binary to Hexadecimal
Shortcut method โ Hexadecimal to Binary
Decimal to Other Base System
Steps
Step 1 โ Divide the decimal number to be converted by the value of the new base.
Step 2 โ Get the remainder from Step 1 as the rightmost digit of new base number.
Step 3 โ Divide the quotient of the previous divide by the new base.
Step 4 โ Record the remainder from Step 3 as the next digit of the new base number.
Repeat Steps 3 and 4, getting remainders from right to left, until the quotient becomes zero in Step 3.
The last remainder thus obtained will be the Most Significant Digit of the new base number.
Example โ
Decimal Number: 29 10
Calculating Binary Equivalent โ
Step Operation Result Remainder
Step 1 29 / 2 14 1
Step 2 14 / 2 7 0
Step 3 7 / 2 3 1
Step 4 3 / 2 1 1
leastsignificantdigit
totheleft
MSD
Step 5 1 / 2 0 1
As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the Least Significant Digit and the last remainder becomes the Most Significant Digit.
Decimal Number โ 29 10 = Binary Number โ 11101 2.
Other Base System to Decimal System
Steps
Step 1 โ Determine the column value of each digit .
Step 2 โ Multiply the obtained column values by the digits in the corresponding columns.
Step 3 โ Sum the products calculated in Step 2. The total is the equivalent value in decimal.
Example
Binary Number โ 11101 2
Calculating Decimal Equivalent โ
Step Binary Number Decimal Number
Step 1 (^111012) ((1 ร 2^4 ) + (1 ร 2^3 ) + (1 ร 2^2 ) + (0 ร 2^1 ) + (1 ร 2^0 )) 10
Step 2 (^111012 )
Step 3 (^111012 )
Binary Number โ 11101 2 = Decimal Number โ 29 10
Other Base System to Non-Decimal System
Steps
Step 1 โ Convert the original number to a decimal number.
Step 2 โ Convert the decimal number so obtained to the new base number.
Example
Octal Number โ 25 8
Calculating Binary Equivalent โ
LSD MSD
positional thisdependsonthepositionofthedigitandthebaseofthenumbersystem
inStep 1
base 10
Step Binary Number Octal Number
Step 1 101012 010 101
Step 2 (^101012 28 )
Step 3 (^101012 )
Binary Number โ 10101 2 = Octal Number โ 25 8
Shortcut method - Octal to Binary
Steps
Step 1 โ Convert each octal digit to a 3 digit binary number .
Step 2 โ Combine all the resulting binary groups into a single binary number.
Example
Octal Number โ 25 8
Calculating Binary Equivalent โ
Step Octal Number Binary Number
Step 1 (^258 210 )
Step 2 (^258 0102 )
Step 3 (^258 )
Octal Number โ 25 8 = Binary Number โ 10101 2
Shortcut method - Binary to Hexadecimal
Steps
Step 1 โ Divide the binary digits into groups of four.
Step 2 โ Convert each group of four binary digits to one hexadecimal symbol.
Example
Binary Number โ 10101 2
theoctaldigitsmaybetreatedasdecimalforthisconversion
of 3 digitseach
startingfromtheright
Calculating hexadecimal Equivalent โ
Step Binary Number Hexadecimal Number
Step 1 101012 0001 0101
Step 2 (^101012 110 )
Step 3 (^101012 )
Binary Number โ 10101 2 = Hexadecimal Number โ 15 16
Shortcut method - Hexadecimal to Binary
Steps
Step 1 โ Convert each hexadecimal digit to a 4 digit binary number .
Step 2 โ Combine all the resulting binary groups into a single binary number.
Example
Hexadecimal Number โ 15 16
Calculating Binary Equivalent โ
Step Hexadecimal Number Binary Number
Step 1 (^1516 110 )
Step 2 (^1516 00012 )
Step 3 (^1516 )
Hexadecimal Number โ 15 16 = Binary Number โ 10101 2
thehexadecimaldigitsmaybetreatedasdecimalforthisconversion
of 4 digitseach
