Representation of Integers

Whenever we enter data in a physical file or paper, there is no complication in how it will be represented there. However, the case is not the same in the case of computers because the applications are different. For example, the representation of real and integers in computers involve significant approximation and a deeper understanding of essential digits concerning how the mathematical operations will proceed. This article deals with the concept of representing integers in the context of computer science.

Representation of Integers in Computer

In computer science, integers are presented in the form of a binary digit. It also refers to its value and representation because it depends on how it is stored in the computer memory. A typical data set in a computer depends on the minimum and maximum possible value derived from it. 

Although the order of memory bytes differs, a specific data set in a computer always has a difference in its minimum and maximum possible value. There are two major types of integer representation: unsigned integers and signed integers. 

The most common representation of integers in computer science is expressed in a string of bits. The width and accuracy of an integral type depend on the number of bits in the representation of integers. 

On the other hand, there are four methods to represent signed numbers in a binary computing system. But some other computer languages also define integer sizes and representation through manual methods that are machine-independent. 

The other perspectives have different definitions depending on the processor word size leading to a different representation of integers in computer science. Therefore, the representation of integers in computers is different from its expression in mathematics. So, it is necessary to understand the critical elements involved that make this difference possible. 

Representation of Integers on Different Bases

In computer science, integers can also be represented on different bases. For example, if we change the number to base ten from another base, we need to break down the value. 

For instance, if we have to change the number 5763, we will have to break it down and write it as: 

5000 + 700 + 60 + 3 

If we notice the above pattern carefully, the digits corresponding to the existing coefficients on the power of 10 are brought together to get the final value. Similarly, we can also specify numbers in other bases except ten for the representation of integers in different bases. 

In this case, we must add the value together to get a final value using different digits corresponding to the coefficient of the powers. In that order, every number will have a base for its representation, but no more than one such representation must be done. Using only the digits 0 by (b-1) in any given base number is recommended. 

Changing From Base 10 to a Different Base

The most common method for conversion of a number from base 10 to a different base includes the following steps:

• Identify the highest power of the base that can go into the number with a non-zero number of times repetition

• Identify how many times it is possible to subtract this power from a given number without making the resulting negative. In other words, divide a number by the power and note down the value obtained

• Recreate the number again in terms of its short position as a positive remainder after dividing by the power

• Repeat the above step with the power you will divide by the base

• Revisit the second step and check if the power is now less than 1. If the power is less than one after dividing the values, you have successfully changed from base 10 to a different base 

Counting the Numbers in Another Base

Counting in other bases is not much different from counting in base 10. However, if the requirement leads us to add another base without converting to base 10, you can easily count the numbers. It is only possible as long as you carry the sum greater than or equal to the original base. 

In such cases, changing numbers from one place to another often leads to erroneous cases that can lead to significant errors in the calculation. Hence, it is necessary to take note of the values before arriving at the final value after calculation.

Conclusion 

The representation of integers in a computer depends on the method adopted for expressing the digits. In this case, integers are represented in the form of a group consisting of binary digits, where the grouping size depends on the set of interior sizes available. Computer hardware makes it possible for the representation to register itself in the memory address in the form of an integer.