The most popular way to convert a decimal number into the binary is the double dabble method. In this method, the given decimal number is progressively divided by 2 and writing the remainder after each division. When all the remainder is read in reverse order, the binary number is obtained.
Steps for Decimal to Binary Conversion
Step – 1 Divide the decimal number which is to be converted by two which is the base of the binary number.
Step – 2 The remainder which is obtained from step 1 is the least significant bit of the new binary number.
Step – 3 Divide the quotient which is obtained from the step 2 and the remainder obtained from this is the second least significant bit of the binary number.
Step – 4 Repeat the process until the quotient remains zero.
Step – 5 The last remainder obtained from the division is the most significant bit of the binary number. Hence arrange the number from most significant bit to the least significant bit (i.e., from bottom to top).
This method can easily be understood by considering an example which is explained below.
For example – Consider the conversion of the decimal number 25 into its equivalent binary.
For fractional decimal numbers, multiply it by 2 and record the carry in the integral position. The carries when read down produces the equivalent binary fraction as explained by the example given below.
Consider the fractional binary number 0.35
The process of multiplication by 2 will continue till the desired accuracy is achieved.
Conversion of Decimal to Binary for Mixed Number
To convert a decimal mixed number into the binary number, the same approach is used, as was done in integer and fractional parts of the number. Consider the decimal number 13.40.
The binary equivalent of 13 is 1101, and the binary equivalent of 0.40 is. 011001. Therefore 1101.011001 is the required binary number.