IBPS Clerk Computer Aptitude : Conversion From Decimal to Binary (vice-versa)

IBPS Clerk prelims are over and it’s time to gear up for the IBPS Clerk Mains exam. We have received a lot of queries asking for : How to convert decimal to binary and vice-versa.

In this post we would be covering this topic- Computer Aptitude : Conversion from Decimal to Binary number system in detail. This post would help you prepare better for the reasoning ability and computer aptitude section of the IBPS clerk mains exam.

IBPS Clerk Mains Computer Aptitude : Decimal & Binary Numbers

When we write decimal (base 10) numbers, we use a positional notation system. Each digit is multiplied by an appropriate power of 10 depending on its position in the number. For example:

843 = 8 x 10² + 4 x 10¹ + 3 x 10⁰
= 8 x 100 + 4 x 10 + 3 x 1
= 800 + 40 + 3

For whole numbers, the rightmost digit position is the one’s position (10 to the power 0 = 1). The numeral in that position indicates how many ones are present in the number. The next position to the left is ten’s, then hundred’s, thousand’s, and so on. Each digit position has a weight that is ten times the weight of the position to its right.

In the decimal number system, there are ten possible values that can appear in each digit position, and so there are ten numerals required to represent the quantity in each digit position. The decimal numerals are the familiar zero through nine (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

In the binary number system the base is not ten (decimal system), but is instead two (0, 1). Each digit position in a binary number represents a power of two. So, when we write a binary number, each binary digit is multiplied by an appropriate power of 2 based on the position in the number. For example:

101101 = 1 x 2⁵ + 0 x 2⁴ + 1 x 2³ + 1 x 2² + 0 x 2¹ + 1 x 2⁰

= 1 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1

= 32 + 8 + 4 + 1 = 45

In the binary number system, there are only two possible values that can appear in each digit position rather than the ten that can appear in a decimal number. Only the numerals 0 and 1 are used in binary numbers.

IBPS Clerk Mains Computer Aptitude: Conversion Between Decimal & Binary

Binary To Decimal : Converting a number from binary to decimal is quite easy. Multiply each binary digit by the appropriate power of 2 and then add them. For example:

Question: Convert (101102)₂ to decimal.

(101102)₂ = 1 x 2⁵ + 0 x 2⁴ + 1 x 2³ + 1 x 2² + 0 x 2¹ + 1 x 2⁰

(101102)₂ = 32 + 0 + 8 + 4 + 0 + 1

(101102)₂ = (45)₁₀

Decimal To Binary : The method for converting a decimal number to binary involves using successive division by the base until the dividend reaches 0. At each division, the remainder provides a digit of the converted number, starting with the least significant digit. For example:

Question: Convert the decimal number 13₁₀ to binary

• Divide 13₁₀ by the system base, which when converting to binary is 2. This gives the answer 6, with a remainder of 1.
• Continue dividing the answer by 2 and writing down the remainder until the answer = 0
• Now simply write out the remainders, starting from the bottom, to give 1101_2.

The following picture illustrates the process more clearly.

Let us look at one more example.

Question: Convert (37)10 to binary.

Step 1:  37 / 2 = 18  Remainder = 1  (least significant digit) (rightmost)

Step 2:  18 / 2 = 09  Remainder = 0 

Step 3:  09 / 2 = 04  Remainder = 1 

Step 4:  04/ 2 = 02  Remainder = 0 

Step 5:  02 / 2 = 01  Remainder = 0 

Step 6:  01 / 2 = 0    Remainder = 1  (most significant digit) (leftmost)

The resulting binary number is 100101.

Hope this helps. Feel free to reach out to us on for any queries or doubts.

All the best!