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NUMBER SYSTEM CONVERSION
Value of one number system can be converted into another. For example, decimal numbers can
be converted into binary numbers and vice-versa.
Decimal to Binary Conversion
To convert a decimal number into a binary number, follow these steps:
Step 1 Divide the decimal number by 2 (the base of the binary number system).
Step 2 Note down the quotient and the remainder.
Step 3 Divide the quotient obtained again by 2 and note down the resulting quotient and
remainder.
Step 4 Repeat the procedure till you reach a quotient less than 2.
Step 5 List the last quotient and all the remainders (moving from bottom to top). You will get
your binary number.
Look at the given examples to better understand the conversion process.
Example 1: Convert the decimal number 26, i.e., (26) to binary.
10
2 26
2 13 – 0 The binary equivalent of (26) is 11010
10
2 6 – 1 In other words, (26) = (11010) 2
10
2 3 – 0
1 – 1
Start listing the last quotient and all the remainders from here.
Example 2: Convert the decimal number Example 3: Convert the decimal number (37)
10
(64) to binary. to binary.
10
2 64
2 37
2 32 – 0
2 18 – 1
2 16 – 0 Binary equivalent: 100101
2 9 – 0
2 8 – 0 (64) = (1000000)
10 2 2 4 – 1
2 4 – 0
2 2 – 0
2 2 – 0
1 – 0
1 – 0
Certainly, let's explore more examples of converting decimal numbers to binary using the
repeated division method.
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