Number System and Conversions

Number systems and conversions are part of computer operation and programming. The number system helps in regulating the operations of the computer. The computer runs on the machine language. It is a program only for the operation of the computer and it is different from our language and communication system. So to ensure smooth communication between human beings and the machine, the number system and conversions are important. The most common questions from the number system and conversions in the competitive exams are the conversions of the binary number into the decimal number and the conversion of the decimal number into the binary digits.

What is a binary number?

The term biliary denotes the use of two numbers. The binary number system operates on the use of 0 and 1. The numbers which are generated further, use these two digits as their basic units.

What is the decimal number?

The term decimal is related to 10, so it operates with the use of 10 numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The numbers which are generated further use these 10 digits as their basic units.

What is a hexadecimal number system?

The term hexadecimal denotes the number 16, so it operates with the use of 10 numbers and six alphabets, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f. The numbers which are generated further use these 16 numbers and alphabets as their basic units.

Converting binary to decimal

To convert a binary number into a decimal number, we have to use the following method. We have to multiply the digits of the number with the powers of 2, increasing one after another and starting from 0, then we have to discard the results from the places where 0 is used in the binary number and we have to add the numbers calculated from the places where 1 is used as a digit in the binary number. It the number is 1001, then we have to multiply the digits with the powers of 2, so the number will be, 1 X 2³ + 0 X 2² + 0 X 2¹ + 1 X 2⁰ = 8 + 0 + 0 + 1 = 9, so while converting binary to decimal, the conversion of the number 1001 into binary number system will be 9 into decimal number system.

Converting decimal to binary

To convert a decimal number into a binary number, you need to divide the number with two if it is an even number and if this is an odd number, you need to subtract one from the number and then divide it with two. The same step has to be followed until 1 is left, then the number should be taken from below to above, and in the place of the odd numbers, 0 is counted.

2 I 7 – 1

2 I 3 – 1

2 I 2 – 0

1

Here we have divided 6, which we have derived by subtracting 1 from 7, with 2, the dividend, 3 could not be divided by 2 and so we again subtracted 1 from it and divided the remaining 2 by 2, since 2 was divisible by 2, we subtracted 0 from it and the remaining number is 1. We shall start from 1 and go upwards while converting decimal into binary. So the binary number will be 1011 if we convert decimal 7 into binary.

The international system of numeration

The international system of numeration is a standardized number system for using statistical data. For, example, the number 32454567 is written as 32, 454, 567 in the International system of numeration. The number, when written in words, will use each section separated by the comma separately. The word will be mentioned as thirty-two million four hundred and fifty-four thousand five hundred sixty-seven.

Conclusion

It is not enough to know the basic information on the number system and conversions, since it only gives a brief knowledge of converting binary to decimal, converting decimal to the binary, international system of numeration, etc. To know more, you need to understand how machine language operates, how the number system is related to the computer system, and how the conversion transmits data. The use of a number system also helps in dealing with quantitative data and provides support for computer operation, which you need to know in detail.