The Basics of the Number System in Computer: Understanding Binary and Decimal

The Basics of the Number System in Computer: Understanding Binary and Decimal

In today’s digital era, computers have become an integral part of our lives. From smartphones to supercomputers, every computing device uses a complex number system to communicate and process information. In this article, we will explore the two fundamental number systems in the computer world: binary and decimal.

Introduction to Number System in Computers:
A number system in computing is a way of representing numbers using specific symbols. The two basic number systems used in computers are Binary and Decimal.

Binary Number System:
Binary is a base-2 number system that uses only two digits, 0 and 1, to represent any number. Computers use binary numbers to store and process information. Each digit in a binary number is called a bit, and eight bits together form a byte, which is the basic unit of storage in computers.

For example, the decimal number 6 can be represented in binary as 110. It uses two bits, and the first bit represents 4 (2^2) and the second bit represents 2 (2^1). We can add the values of these bits to get the total value of 6.

Likewise, the decimal number 34 can be represented in binary as 100010, using six bits. The leftmost bit represents 32 (2^5), whereas the rightmost bit represents 2 (2^1).

Decimal Number System:
Decimal is a base-10 number system that uses ten digits, 0 to 9, to represent numbers. It is the most common number system used by humans, and we are most familiar with it. In the decimal system, each digit represents a power of 10. For example, the number 1234 in decimal form is calculated as (1×10^3)+(2×10^2)+(3×10^1)+(4×10^0) = 1000+200+30+4.

Converting Binary to Decimal:
Converting binary numbers to decimal numbers is easy. You simply need to multiply each bit by its corresponding power of 2 and add all the results. For example, the binary number 1101 can be converted to decimal by calculating (1×2^3)+(1×2^2)+(0x2^1)+(1×2^0) = 8+4+0+1 = 13.

Converting Decimal to Binary:
Converting decimal numbers to binary numbers is a bit more complex, but the process is straightforward. You need to divide the decimal number by 2 repeatedly until you get 0. You then take the remainders of each division, starting from the last one, to form the binary number. For example, the decimal number 54 can be converted to binary by dividing it by 2 repeatedly as follows: 54/2=27 (remainder 0), 27/2=13 (remainder 1), 13/2=6 (remainder 1), 6/2=3 (remainder 0), 3/2=1 (remainder 1), 1/2=0 (remainder 1). The remainders read from bottom to top give the binary number 110110.

Conclusion:
In conclusion, understanding the basics of the number system in computers is essential to perform any task in the digital world. Binary and decimal are the two primary number systems in computing. Computers use the binary number system for all their operations, but humans use decimal. Converting between the two number systems is not difficult, and it is necessary to know how to do so. With this knowledge, you can write codes, analyze data, and perform various other tasks in the digital world.