Binary Numbers: What Are They and How Do They Work?

2024-03-27 | By Sarah Aman

In the current digital age, binary numbers are the unsung heroes that power the technology we rely on daily. Understanding how binary numbers work is a fundamental part of comprehending how technology works. Let’s take a closer look at binary numbers, what they are, how they work, and their crucial role in the world of technology.

What Are Binary Numbers?

Binary Numbers are a base-2 numeral system, in contrast to our everyday decimal system, which is base-10. In the decimal system, we use ten digits (0-9) to represent all numbers. Binary employs only two digits: 0 and 1. This may seem simplistic, but it’s the foundation upon which digital systems are built.

The Binary Counting System

Counting in binary is similar to counting in decimal, with each digit representing a place value. In decimal, you have units of ones, tens, hundreds, and so on. In binary, you have units of ones, twos, fours, eights, and so forth, doubling in value as you move to the left. To better understand, let’s compare some decimal and binary numbers side by side:

Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

Binary: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010

We can see that in binary, two is represented by 10, and three is represented by 11. This simple pattern makes binary numbers easy to comprehend and mathematically manipulate.

Binary Operations

Just as you can perform arithmetic operations like addition, subtraction, multiplication, and division with decimal numbers, you can do the same with binary numbers. The key difference lies in the binary addition table, where 0 plus 0 equals 0, 1 plus 0 equals 1, and 1 plus 1 equals 10 (binary for 2 in decimal). To add binary numbers, follow a similar process to decimal addition, carrying over when the result is 2 or greater:

101 (5 in decimal)

110 (6 in decimal)

= 1011 (11 in decimal)

Binary subtraction and multiplication work in a similar way, albeit with the specific binary rules for 0s and 1s. Division is also possible but can be more complex due to the different place values involved.

Binary and Computers

Binary numbers are the language of computers. Inside your computer, data is processed and stored in binary format. Every piece of information, from text and images to code and instructions, is represented using a combination of 0s and 1s.

Transistors, the building blocks of computer hardware, have two states: on (1) and off (0). By manipulating these states, computers can process, store, and transmit vast amounts of data at remarkable speeds. It's the binary system's simplicity that makes it ideal for this purpose.

Conclusion

Binary numbers are the backbone of modern computing, and understanding how they work is essential for anyone interested in technology or programming. By embracing the simplicity of just two digits, 0 and 1, binary numbers provide the foundation for the complex and powerful devices we use daily. Whether you're a computer scientist or simply curious about the inner workings of technology, binary numbers are a fascinating and crucial concept to explore.