Decoding the Digital World: An Introduction to Binary Language Basics

We live in a world increasingly driven by computers. From smartphones to supercomputers, these machines process information using a language fundamentally different from how humans communicate. That language is binary code. Understanding the basics of binary can unlock a deeper appreciation for how computers work and pave the way for exploring computer science. Binary code is the bedrock of all coding languages today.

Number Systems: Beyond Decimal

Humans typically count in decimal, a base-10 system. This means we use ten distinct symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to represent all numbers. The reason for this is that the decimal system is the most straightforward number system to perform basic arithmetic.

However, base 10 isn't the only way to count. Duodecimal, or base-12, was once a popular system, evident in units like 12 inches to a foot, 12 pence to a shilling, 12 zodiac signs, and 12 months in a year. Duodecimal maths would use twelve symbols to represent numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B).

The Binary System: A Computer's Native Tongue

Computers don't have fingers to count, nor do they perform mental arithmetic like humans. Instead, they rely on electricity. Their logic circuits operate using "on" and "off" states, making binary, or base-2, the natural counting system for computers. Binary is known as a "base 2" system because it uses two numbers to represent any quantity; in contrast, decimal systems use 10 digits (0-9).

This means they only use two symbols to represent all numbers: 0 and 1. Binary is a numerical system that uses two digits, usually represented as 0 and 1. It is the basis of all digital computers and is used to represent data or instructions in a machine-readable form.

Understanding Binary Representation

In binary, the position of each digit (or "bit," short for binary digit) is crucial. For whole numbers, the most significant bit is on the left, and the least significant bit is on the right. The least-significant digit in a number is the digit that has the smallest influence on a number’s ultimate value. As we move from right to left, each bit represents a higher power of 2 (because binary is base 2). As with any numbering system, use more digits and you can represent bigger numbers.

Binary usually starts at 0. This is because the binary number system works differently from the decimal system we are used to in everyday life. In the decimal system, counting starts from 1 and each number has a value of 10 times the previous number. In binary, counting each number has a value of double the previous one - for example two is two ones, three is two ones with a zero, four would be two zeros with a one and so on. The first number in binary is always zero = 00 and this continues on until infinity.

Example:

The binary number 1011 can be broken down as follows:

1 (leftmost bit) represents 2^3 = 8
0 represents 2^2 = 4
1 represents 2^1 = 2
1 (rightmost bit) represents 2^0 = 1

Adding these values together (8 + 0 + 2 + 1) gives us 11, which is the decimal equivalent of the binary number 1011.

Representing Different Types of Numbers

Binary can represent more than just positive whole numbers.

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Fractional/Floating-Point Numbers: By adding a notional point, we can represent fractional or floating-point numbers in binary.
Negative Numbers: Representing negative numbers in binary can be more complex. There are several methods, including:
- Sign Bit: Using a spare bit on the left to indicate the sign (e.g., 0 for positive, 1 for negative). So, if 00111 is 7, then 10111 is -7.
- Two's Complement: The most common approach in computers. To represent a negative number, you invert all the bits and add 1. For example, if 00111 is 7, then 11000+1 = 11001 represents -7. To flip the sign, invert the bits and add 1 again: 00110+1 = 00111.

Binary Code and Computers

Binary code is an important part of how we communicate with computers. All of your computer’s memory is stored in binary, organized into bytes. Each byte is typically a sequence of eight bits and each bit is either a 1 or a 0. These combinations of 1s and 0s are a binary numbering system that represents higher concepts like letters and numbers. Each of these combinations of eight 1s and 0s ‘bytes’ represents a decimal number, which in turn represents an American Standard Code for Information Interchange (ASCII) code for each letter and character. Computers use the ASCII system to turn these numbers into letters for ‘Happy’ and ‘Coding!’. This is how you read binary code. In this example, ‘Happy’ is equal to five bytes and each byte represents one letter of the word. Similarly, ‘Coding!’ is broken into seven bytes.

Binary is a way of representing data and instructions by using ones and zeros. It is the backbone of all information processing within computers. Each one or zero is referred to as a bit, and every combination of bits can represent a different number, character, data type or instruction used by computers. By combining bits together in various combinations, complex calculations can be made to solve many problems or process instructions.

Binary data is used by computers in several areas; such as generating statistics, mathematical computation, and of course, computer science. It is essentially the primary language of computing systems. The data itself is identified as binary because it only uses two possible states, 0 or 1. The specific location and sequence of the numbers may seem impossible to decipher, but for computers, the base-2 system makes it possible to generate and store endless amounts of information. Binary data works within the parameters of a base-2 counting system. What this means is that there are only two numerical options for the data; either 0 or 1. While this may seem limiting, it’s actually allows our computers and smart devices to complete a seemingly endless array of tasks. The use of a base-2 system for computer data storage can be best attributed to early computer design. Engineers and computer scientists needed a way to communicate with computers and to allow devices to communicate between each other. In computer science, a ‘bit’ is the simplest form that data can take. The name actually comes from combining binary and digit, to represent the logical state with either a 0 or a 1. When several bits are strung together, they form what is known as a ‘byte’. A byte is typically made up of eight bits, and is used as a unit of digital information. To count in binary, think about the typical way we count in our base-10 system. 000, 001, 002 … In a base-2 system, it’s a similar concept except there are only two possible digits: 0 or 1.

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Data Storage: Binary is the foundation for storing all types of information on computers, including images, audio, basic functions, operating systems, and other data.
Executable Files: Binary files contain instructions for specific programs and can be executed by applications capable of handling them. When a user executes a binary file, the instructions are converted into machine code that the computer's processor can understand.
Data Representation: Binary sequences can represent a wide variety of information, from simple values like numbers and strings to complex data such as images, audio files, and executable code.

Binary is important because it allows for the efficient storage and processing of data. It also provides a universal language for communication between computers and other digital devices, allowing them to interact with one another. Binary code enables us to quickly identify errors in data processing or transmission, as well as identifying potential areas of improvement. Additionally, binary code makes it easier to design complex systems that are compatible with different hardware and software components. Furthermore, binary is often used in cryptography as a way to securely communicate between two parties without having the need to share the same physical space.

Is Learning Binary Essential for Developers?

While binary language is often taught as a part of computer science fundamentals, it’s more of an introduction to how computers work. People almost never actually write binary.

Learning binary code is not an important step to becoming a developer. A good analogy to coding in binary before becoming a developer yourself is like learning the composition of a road before learning how to drive. Most drivers do not need to know how the roads are built in order to be good drivers. There is almost no programming career that’ll require you to learn binary. One wonders, then, why learn binary at all? While it isn’t important to learn binary code and it will probably not contribute to your career advancement, you may find intellectual satisfaction in the process. The only time binary would be useful to your career is if you are working in a very specific field. Examples include programming hardware-level processors or onboard microcontrollers.

Today most software developers do not need to know how their software communicates with the hardware. The higher-level programming languages have made development easier. Hence, there is no need to learn the binary system in most cases.

Manipulating Binary Values

There are a number of ways to manipulate binary values. Just as you can with decimal numbers, you can perform standard mathematical operations - addition, subtraction, multiplication, division - on binary values. Bitwise operators perform functions bit-by-bit on either one or two full binary numbers. They make use of boolean logic operating on a group of binary symbols. The complement of a binary value is like finding the exact opposite of everything about it. The complement function looks at a number and turns every 1 into a 0 and every 0 becomes a 1.

OR: OR takes two numbers and produces the union of them. Here’s the process to OR two binary numbers together: line up each number so the bits match up, then compare each of their bits that share a position. For each bit comparison, if either or both bits are 1, the value of the result at that bit-position is 1. For example to find the 10011010 OR 01000110, line up each of the numbers bit-by-bit. Think of the OR operation as binary addition, without a carry-over.
AND: AND takes two numbers and produces the conjunction of them. The process of AND'ing two binary values together is similar to that of OR. Line up each number so the bits match up, then compare each of their bits that share a position. For each bit comparison, if either or both bits are 0, the value of the result at that bit-position is 0. For example, to find the value of 10011010 AND 01000110, start by lining up each value. Think of AND as kind of like multiplication.
XOR: XOR is the exclusive OR.
Bit Shifts: There are two components to a bit shift - the direction and the amount of bits to shift. When shifting to the right, one or more of the least-significant bits (on the right-side of the number) just get cut off, shifted into the infinite nothing. Shifting to the left adds pushes all of the bits toward the most-significant side (the left-side) of the number. That simple bit shift actually performs a relatively complicated mathematical function. Shifts to the left n bits multiplies a number by 2n (see how the last example multiplied the input by two?), while a shift n bits to the right will do an integer divide by 2n. Shifting to the right to divide can get weird - any fractions produced by the shift division will be chopped off, which is why 154 shifted right twice equals 38 instead of 154/4=38.5.

These bitwise operators provide us most of the tools necessary to do standard mathematical operations on binary numbers.

A Brief History of Binary Code

Although computing systems are a relatively new invention, binary is not. Binary code - as we understand it today - was initially discovered in the 17th Century by German Mathematician Gottfried Wilhelm Leibniz. The binary system that you know today was invented in the 17th century. It was developed and proposed by Gottfried Wilhelm Leibniz, who created it around 1679 and published it in 1703.

As humanity and our technology advanced through the centuries, the use of binary became more and more prevalent as a way to collect and store data. One of the most famous examples of this comes from the 16th Century Philosopher Francis Bacon. Bacon devised a system that he called, ‘Bacon’s Bilateral Cipher’, which he used to send encrypted messages to trusted friends and adversaries. The main difference between Bacon’s binary and modern binary code, is its use of letters instead of numbers.

When German Mathematician Gottfried Wilhelm Leibniz encountered and eventually grew frustrated with the trials and errors of current data methods, he proposed a base-2 numerical system that could represent the numbers in the decimal system. The simplicity of this new method allowed Leibniz to abandon multiplication tables and, instead, take advantage of rudimentary calculations as he progressed through his work.

To reach our modern understanding of binary code, we have to take a look at the original design of computers. The use of a base-2 counting system can be attributed to the original ‘On’ and ‘Off’ lever that controlled electrical impulses to a computing system. As the basic function of data communication for computational systems, binary code is present in most of our daily activities.

Learning Resources

There are a lot of binary code classes that you can take to help ease your learning journey. Udemy, for example, offers a two-hour lesson called Binary: The Foundation of All Computing that you can take for $25. If you’re wanting a nice introduction that comes highly rated, here are some books on binary code you can check out: Understanding Binary Numbers by Erik Sakk, Binary, Octal and Hexadecimal for Programming & Computer Science by Sunil Tanna, or Advanced Binary by Sunil Tanna.

Free Binary Tutorial by CodeConquest, for example, lays out the basics of binary and potential applications of binary in an easy-to-understand manner. However, if you are looking to master binary, programs that are more in-depth and guided are highly recommended.

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