Number System Conversions form an important part of the banking exams. In the computer awareness section, the knowledge of the binary number system and other number systems is not only basic but critically important for a good score. Here we will see methods of conversion between various number systems like binary, decimal and others.

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## Number System Conversions

In the topic on number systems, there are different types of number systems. All of them have their specific properties and rules that define them. As a result of these properties, we see that we can convert a given number from one number system to another. Let us begin with the conversion of numbers in the binary system and numbers in the binary system.

### Representation of Number systems

Numbers belonging to various number systems are represented in a specific manner. To represent the number that belongs to a given number system (say the decimal number system) we write the number in braces and put the base number in subscript outside the braces. For example, 22 in the decimal system can be written as (22)_{10}. The same number in the binary number system can be written as (10110)_{2}. Let us see how we convert from one number system to another.

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### Decimal To Binary

In the decimal system, the base is 10 and every number is written as a combination of the powers of 10. Any integral number in the decimal system when divided by 2, will either leave a remainder of 0 or 1. Thus division by zero is a way to represent such numbers as a series of 0’s and 1’s. Therefore, to convert from decimal to binary, we keep dividing by 2 and go on recording the remainders. Let us see an example.

Example 1: Convert the number 22 from decimal to binary.

Let us start dividing by 2 and noting the remainders.

2 | 22 | 0 |

2 | 11 | 1 |

2 | 5 | 1 |

2 | 2 | 0 |

1 |

Starting from the 1 at the bottom, we can write a series of 1’s and 0’s as 1, 0, 1, 1, 0. This gives the binary equivalent of the number 22. Therefore, we write the binary equivalent of 22 as 10110. If done in this way, the remainder of the first step becomes the LSD (least significant digit) whereas the remainder of the last step becomes the MSD (Most Significant Digit).

In short, if you have to convert from decimal to any number system, you should divide the number by the given base (e.g. 16 or 8 etc.).

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### Binary to Decimal

If you have been careful, you must have noticed that the way to represent a decimal number from its binary counterpart is a reversal of the above. Therefore, what we need to do is take the binary equivalent of the number and multiply each binary digit with a power of two; where the power of 2 is derived from the place value of the binary digit. For example, let us convert 10110 from binary to the decimal. We already know the answer to this!

10110 = Starting from the right, count the number of the digits from 0 to onwards. The digit at the extreme right is the LSD and is multiplied by 20. Similarly, the digit right next to the LSD (here =1), is multiplied by 21 and so on until we get to the MSD as shown below.

1×2^{4} + 0×2^{3} + 1×2^{2} + 1×2^{1} + 0×2^{0} = 16 + 0 + 4 + 2 + 0 = 22 as was expected.

## General Method

If you have understood the logic behind the conversion from one number system to another, you must have guessed the rules already. Let us sum up these rules below.

### Decimal To Other Base System

The following steps follow as a natural consequence of the conversion of any decimal number to other systems with a different base (e.g. binary has a base of 2).

1: Take the decimal number that you want to convert (say 22), and divide by the number of the new base (say 2 for binary).

2: The digit that is the remainder of the first step is the LSD.

3: Keep on dividing and noting the remainders, until the quotient is zero.

4: The remainder of the step where the coefficient is zero is the most significant digit or the (MSD).

### Other Base System To Decimal System

We can use similar logic to convert from other number systems to binary. The following rules could be useful while changing from other base systems to the binary system.

1: Count the number of digits that are in the number that is to be changed from one system to another.

2: Multiply these digits by the power of the base raised by its position (as done above), starting from zero.

3: Find the sum of this product. The sum is your answer.

These two general rules shall help you convert any given number into another number system. Normally a decimal to binary conversion appears in the exam. Other conversions are very infrequent. We urge you to practice on a lot of numbers to find the conversions and get better at them. Here in the next section, we have included some of these questions.

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## Practice Questions

Q 1: The binary equivalent of 1 is

A) 01 B) 00 C) 10 D)0

Ans: 01

Q 2: The binary equivalent of 2 is

A) 10 B) 11 C) 0 D) 10

Ans: 10

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