How to Understand Binary Systems? A Beginner’s Guide

In this article, we’ll explore the concept of binary systems and provide a step-by-step guide on how to understand and work with them.

What is a Binary System?

A binary system, also known as a base-2 system, is a number system that uses only two digits, 0 and 1, to represent numbers. This is in contrast to the decimal system, which uses 10 digits from 0 to 9. Binary systems are commonly used in computer programming and electronics because they are well-suited for electronic circuits that can only be in one of two states: on or off, high or low, true or false.

How Binary Systems Work

In a binary system, each digit, or bit, can have one of two values, 0 or 1. This allows for the representation of numbers using only two digits. Here’s an example:

• The decimal number 5 is represented as 101 in binary (1 × 2^2 + 0 × 2^1 + 1 × 2^0).
• The decimal number 12 is represented as 1100 in binary (1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 0 × 2^0).

Converting Decimal to Binary

Converting decimal numbers to binary is a simple process. Here’s a step-by-step guide:

1. Divide the decimal number by 2.
2. Note the remainder, which will be either 0 or 1.
3. Repeat step 1 with the quotient until it becomes 0.
4. Write down the remainders in reverse order, starting from the bottom.

For example, let’s convert the decimal number 15 to binary:

1. Divide 15 by 2, remainder 1 (15 = 2 × 7 + 1).
2. Divide 7 by 2, remainder 1 (7 = 2 × 3 + 1).
3. Divide 3 by 2, remainder 1 (3 = 2 × 1 + 1).
4. Divide 1 by 2, remainder 1 (1 = 2 × 0 + 1).
5. Write down the remainders in reverse order: 1, 1, 1, 0.

The binary representation of 15 is therefore 1111.

Converting Binary to Decimal

Converting binary numbers to decimal is also a simple process. Here’s a step-by-step guide:

1. Multiply each bit by the corresponding power of 2.
2. Add up the results.

For example, let’s convert the binary number 1010 to decimal:

1. Multiply 1 × 2^3 = 8.
2. Multiply 0 × 2^2 = 0.
3. Multiply 1 × 2^1 = 2.
4. Multiply 0 × 2^0 = 0.
5. Add up the results: 8 + 0 + 2 + 0 = 10.

The decimal representation of the binary number 1010 is therefore 10.

Conclusion

In conclusion, binary systems are a fundamental concept in computer programming and electronics. Understanding how to convert decimal numbers to binary and vice versa is essential for working with binary systems. By following the step-by-step guides provided in this article, you should now be able to convert between decimal and binary systems.