Computers translate the inputs given to them by converting them into sequences of 1’s and 0’s. This mysterious representation can be reversed so that the encoded texts and numbers can be read. There are specific binary numbers that are assigned to symbols and numbers following international conventions, such as ASCII and Unicode.
We rely on computers to handle many of our tasks. There is a system in place: we provide input, the computer processes it, and gives us the desired output. The information that is readable by humans is converted into something that the computer understands, which is the binary system’s sequences of information in the form of 1’s and 0’s.
You have probably come across these unintelligible sequences of 1’s and 0’s and couldn’t make sense of what is happening. However, just as readable information can be converted into binary, binary can be converted into plain English without the use of computers!
All computer processes can be broken down into sequences of binary (Photo Credit : Fotomay/Shutterstock)
We can understand the binary language, but to do that we need to comprehend the numerical system.
Numerical Systems
Modern computers are powered by electricity. These computers process the incoming information from the electricity in the microprocessors. There are two states of electricity: on and off. These on and off states of electricity are represented by 1 and 0—the binary system of computer science.
Binary is a numerical system, similar to the decimal system (base 10), which we use in our everyday lives. It is actually quite similar to the decimal system in many ways.
Decimal System
We use 10 symbols to count, that is, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We do not add any more symbols after 9, as it would be very difficult to remember a unique symbol for every possible number. Instead, we add a decimal to the left, making the number after 9 into 10. This is known as positional notation.
Ten symbols in the decimal system (Photo Credit : EgudinKa/Shutterstock)
In the decimal system, when we reach 10 or an exponent of 10, we add a number to the left of the decimal. For example, as we reach 9, it becomes 10, and as we reach 99, it becomes 100, and so on. Each new exponent is 10 times bigger than the previous one, such as 10, 100, 1000, 10000, 100000, and so on.
Addition in the decimal system is straightforward: consider 132 + 49. We start from the right and add 9 and 2, giving us 11, so we carry the extra one to the next unit.
We then add the next decimal, 3 + 4, and the carried over 1, giving us 8. The sum of 132 + 49 is 181.
Binary System
Unlike the decimal system, which uses 10 symbols, the binary system is simpler and uses only two symbols, 1 and 0. As each new exponent in the decimal system becomes 10 times bigger, the next exponent in the binary system is 2 times bigger.
Each bit doubles the one on its right
Take the binary number 10. It has 0 in its first exponent, so it is 0 (binary) x 1 (exponential) = 0. It has 1 in the second exponent, so it is 1 (binary) x 2 (exponential) = 2. Therefore, the binary number 10 represents 2.
The concept of binary representation is quite simple. When it comes to addition, the process is similar. Let’s take the binary numbers 101 and 11 as an example. In binary, we can only use two variables: 0 and 1. We start the addition from the right-hand side. When we add 1 and 1, we get a sum of 2. However, we can’t write 2 in binary, so we represent it as 10. We keep the 0 and carry the 1 to the next exponent. Next, we add 1 + 0 + 1, which gives us 2. Again, we represent it as 10 and carry the 1 to the next exponent. Continuing this pattern, we add 1 + 1, which gives us 2. Since there is nothing to carry on to, we keep the complete binary representation and get the sum as 1000. To verify our answer, we convert the binary numbers back to the decimal system. 101 is equal to 5, 11 is equal to 3, and 1000 is equal to 8.
Basic binary addition
Understanding Binary Numbers
Now that we have a basic understanding of how binary numbers work, we can learn how they represent information and read them without the use of a computer.
How to Interpret Numbers
We know that binary numbers use only two variables and each exponent is twice as big as the previous one. We have seen how small numbers are represented in binary, and their binary string is short (2 is 10). However, using only two variables means that larger numbers have longer binary representations.
Whole Numbers
Let’s consider the number 11110011:
Each number is double the number on its right side. As shown in the image above, each binary number must be multiplied by its corresponding exponent and added together to get the decimal value that the binary number represents. So, starting from the rightmost digit; (1 x 1) + (1 x 2) + (0 x 4) + (0 x 8) + (1 x 16) + (1 x 32) + (1 x 64) + (1 x 128). This equals 1 + 2 + 0 + 0 + 16 + 32 + 64 + 128 = 243.
Breaking down an 8-bit binary code
The example above uses 8 bits of binary, also known as an 8-bit. 8-bit systems are commonly used and referred to as a byte. The maximum value an 8-bit can hold is 256 (11111111) and they were used in the early personal computers with 8-bit graphics and audio. These computers performed most operations using 8 bits.
Decimal Numbers
The 8-bit system has limitations in terms of size, so larger bit systems have been developed to address this issue. These systems are 32 bits and 64 bits. The largest number that can be represented by 32 bits is 4,294,967,295 or 4.3 billion! However, even this has limitations for representing much bigger numbers, which is where 64-bit computing comes in, a very common bit system used in computers today. The largest number that can be represented by 64 bits is 18,446,744,073,709,551,615 or 18.44 quintillion—a very large number!
These larger systems are important when representing decimal numbers like 182.68. These numbers are called floating-point numbers, as the decimal point can be shifted anywhere, e.g., 182.68 can be represented as 0.18268 x 103.
Various systems have been developed for representing numbers in binary; the most commonly used one today is the IEEE 754 Standard. This method uses scientific notation to store floating-point numbers. Every decimal number must be in the form of 0.18268 x 103.
Let’s consider the number 1.5:
In floating-point notation, 1.5 would be represented as +1.5 x 100. Following the 32-bit IEEE system, the number is broken down into three parts. Firstly, the sign of the number, which can be positive or negative, indicated by 1 (negative) or 0 (positive). Next, the exponent 100 and the mantissa 1.5 are represented in their binary counterparts. So, +1.5 x 100 becomes 0-0111111-100000000000000000000000.
Representation of floating-point in 32-bit binary
How to Interpret Text
The most commonly used languages and symbols for binary representation are ASCII (American Standard Code for Information Interchange) and UNICODE.
Each symbol corresponds to an 8-bit number length in ASCII.
The process of reading binary text is straightforward. The binary text is divided into 8-bit chunks, which represent individual symbols or letters. The corresponding symbol for each 8-bit chunk in the ASCII table is noted, and the sentences are formed, similar to solving a puzzle.
An ASCII table with symbols and their corresponding binary code. (Photo Credit: cristi180884/Shutterstock)
Let’s consider the following binary text: 01001001 00100000 01101100 01101111 01110110 01100101 00100000 01110000 01101001 01101110 01100101 01100001 01110000 01110000 01101100 01100101 01110011 :
I have already organized the chunks so it is a little less confusing. Each character is searched for in the ASCII table and the corresponding symbol is recorded. It is important to note that the computer also needs to be instructed to add spaces between each word, which requires another symbol.
The symbols mentioned above can be translated into the sentence “I love pineapples”.
The same process can be applied to interpret any block of binary code as text. Unicode has adopted all the characters from ASCII and has expanded its library to include symbols from various languages around the world, even including emojis! You can find all the characters here.
In Conclusion
Binary is the fundamental unit of computing, the basic components of every operation that occurs within a computer. Every image, video, and gif is represented as a long sequence of 1’s and 0’s, including the text you are currently reading on this website!
Understanding how to read binary provides insight into what happens behind our screens and how we communicate instructions to computers. It serves as the link between the physical and the digital realms.