Believe it or not, the most powerful numbers in the world of computers are zero and one. Now that you know that, then you might not want to continue reading this article. The thing is we haven’t asked the real questions of “why” and “how.”
The reason for 0 and 1 to be the most powerful numbers in the computing world is because these two numbers determine the value or data that is processed by the processor. Our computing devices have evolved from a one-room calculator (ENIAC – Electronic Numerical Integrator and Computer) to the latest smartphone that we are using. All of these computers have one thing in common – they all use the principle of the binary system – the numeral system that uses 0s and 1s.
Do we even have to know about how the binary system works in the computers? Some would say, “I will let the engineers who designed and manufactured the gadgets do the thinking as long as the device can do what I want it to do.” That may be true, but let us try to look at a different perspective. When we have a human partner in life, we wanted to know and understand more about that person for us to really appreciate or work the relationship with that person. The same is true with our smartphones, tablets, laptops, and desktops. The more we understand how it works, the more we appreciate the technology that we have.
So, how is the binary system used by computers? We have to understand first how the binary system works before we can understand how this works in the computing process.
We normally use the decimal system – the numeral system that uses the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We also use the place value that holds these numbers. For example, for the number 368, we multiplied 3 in the place value of hundreds, multiplied 6 with the tens, and multiplied 8 with the ones. We don’t usually think of this because we are used to counting in the decimal system, but we have to understand this in order to understand the binary system. Writing it down into math formula, 368 will look like this – (3 x 100) + (6 x 10) + (8 x 1). Lastly, the word “decimal” refers to 10. That means, we are using 10 numerals and we increase the place values by multiplying 10 to itself (100 – ones, 101 – tens, 102 – hundreds, and so on).
The binary system applies the same principle as the decimal system, but the difference is that the binary system uses only two numerals (0 and 1) and has the place value that is multiplied by 2s (20, 21, 22, 23, 24, 25, and so on). The picture below has examples of how numbers are translated into binary numbers.
Converting the decimal system into the binary system is quite simple, but we have to follow the rules properly. Let us convert 38610 (we use bases in order for us not to interchange the values from the decimal system with the binary system because 10110 is not the same as 1012). We need to divide 386 by 2 then get the remainder. So, 386/2 = 193 remainder 0. We divide the quotient, which is 193, with 2 again and get the remainder. We keep dividing the quotient and always writing the remainder until we get a quotient of 1, then that is the time we stop dividing. Now 193/2 = 96 remainder 1. Then 96/2 = 48 remainder 0, 48/2 = 24 remainder 0,24/2 = 12 remainder 0, 12/2 = 6 remainder 0, 6/2 = 3 remainder 0, and last is 3/2 = 1 remainder 1. We get the last quotient which is 1 then write the remainders, in order, from the remainder of 3/2 until 386/2. This will give us 1100000102, which is equivalent to 38610. Another example of how to convert a decimal number into a binary number is shown in the picture below.
Now let us try doing the opposite of converting the binary system into the decimal system. Let us use the same example because we already know the answer. The number 1100000102 has 9 digits. We will separate each of the digits according to the place value of the binary system. Similar with the place value in the decimal system, we begin on the right-most digit and increase to the left. The first digit, which is 0, is placed in the place value of 20 or 1. That means 0x1 = 0. The second digit, which is 1, is placed under 21, which translates into 1×2 = 2. The next 5 digits are all zeroes, so that means we get a product of zeroes to all the place values that hold them. Meaning 22, 23, 24, 25, and 26 will hold 0’s because any number multiplied by zero has a product of zero. The remaining 2 digits have 1 in the place values, so we have to multiply one according to the place value. 27 is the next place value, so 1×27 or 1×128 = 128. The last is 1×28 or 1×256 = 256. We now add all the products, which is 2 + 128 + 256 = 38610. Another example is shown in the illustration below.
Now that we have a glimpse of how the binary system works, we can understand how the engineers who built the first computers worked their magic. Computers – old or new, big or small, simple or complex – needed one thing, electric power. Without this power, our computers are useless. 0s represent “off” and 1’s represent “on.” The image below is a representation of how the computers work with each person holding a one (red) or a zero (white).
The computers that we are using are constantly changing their values with ones and zeroes depending on the data we entered or data that is being processed. Every color, every letter, every sound, every touch, and everything we do with our computers has a corresponding value in the binary system. The microchips, the transistors, the memory, and the processor all convert the electrical power into 1s and 0s and change them into what you are reading right now.
Tennis Crowd (https://www.quora.com/How-does-the-crowd-create-these-kinds-of-displays-to-support-their-team)
Decimal to Binary (https://www.wikihow.com/Convert-from-Decimal-to-Binary)
Binary to Decimal (https://www.wikihow.com/Convert-from-Binary-to-Decimal)
Decimal-Binary Table (http://www.tpub.com/neets/book13/53a.htm)