Human language
Thanks to our intelligent design, humans communicate in words and count in numbers. We build impressive words and numbers by stringing together individual symbols in particular sequences, like DNA strands. In the English language, DNA uses four symbols (A,G,C,T) in many different sequences to show how impossible it is to be just like everyone else.
Western letters
In Western societies, we have 26 letter symbols to string together any way we want. Big Bird on Sesame Street once saw this set of symbols on a sign and sang it as one whole word. I am proud to say I can still do that to this day.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Decimal numbers
Also in Western societies, we have 10 number symbols to string together any way we want. We call that set of numbers ‘decimals’ because ‘deci’ means ten and there are ten number symbols.
0 1 2 3 4 5 6 7 8 9
We added a bunch more symbols, too, like # $ % @. We only know what those characters mean in our own language because successful societies agree to maintain reliable patterns for effective communication. We use our symbols to give or receive information, so it needs to mean the same thing to both parties. We use the information to navigate our lives. We navigate our lives by moving our limbs and taking action on the information we receive.
Symbols to action
God designed an amazing human brain that connects those symbols into words, thoughts and inventions. He added an amazing network of electrical lines connecting our thoughts to our limbs and giving us the power to move and write and speak and build things.
Humans build impressive machines using decimal numbers. Humans built machines that receive, hold, and send more information than any human could ever process. But God did not give an amazing brain to machines. Instead, we try to build it ourselves using materials that can carry electricity like our our brains and nerves. A company called Neuralink is building a machine that will carry our electrical thoughts to machines.
How can we make our machines move and do things when they don’t understand our words?
They don’t have to understand. They can’t help but move when they receive an electrical current. I know how that feels. Has your doctor ever stuck a TENS unit on you?
In the 1800s, humans started connecting electricity to machines. Machines that are controlled by electricity only know two words: ON and OFF. The light bulb receives electricity, it’s on. The electricity stops, it’s off.
Binary numbers
In the 1900s, humans found ways to string ON and OFF in sequences to make machines do more things. For a human to read or write the sequence, we’d have to write ON and OFF many, many times. To write these strings more concisely, they used our number 1 as a symbol for ON and our number 0 for OFF. They strung 1s and 0s together in many different combinations like DNA strands. They put templates in a machine and fed it matching strings of ON (1) and OFF (0). This enabled humans to build machines that do much more than turn on and off. These machines with ON/OFF templates in them are called ‘electronics’.
The machine language made up of 1s and 0s is called ‘binary’. Bi means two, and that language only has two symbols: 1 and 0. If I tell my laptop to type my name, it doesn’t respond. But if I give that laptop the right combination of ON and OFF, it will give me some letters. The keyboard converts my letters to binary strings for me. Here is my name in the binary language of ON (1) and OFF (0):
A – 01100001
M – 01101101
Y – 01111001
AMY – 01100001 01101101 01111001
No, I didn’t type all that out. I once tried to memorize the binary code for each letter, but it got old fast. Here’s a nice little translator where you, too, can see your name in binary. You can use it to name your papers in computer classes and see if the instructor can read it. Next time you see someone with a tattoo like that, you can assume they are a computer nerd and not a robot.
Wouldn’t you think that the first letter of the alphabet would be a number 1? Nope. Numbers come first. It took a lot of 1s and 0s to get through all the number templates and reach the letter templates. Here’s a nice chart that shows how the numbers already claimed the first combinations. All the letters need eight digits, and even those are different for uppercase and lowercase.
Luckily, when a computer displays text for human eyes, it converts its binary strings into the number and letter symbols that we understand. You might have accidentally stumbled upon a computer screen in its birthday suit and seen a bunch of 0s and 1s. You weren’t supposed to see that.
Four number systems
Fast forward to 2025. Humans have built more machines that can receive information in ways other than ON and OFF. We have digital meters and handheld lasers and my God-given robot vacuum named Cory. They are all programmed with specific sequences of numbers, but binary isn’t the only system now.
There are currently four main number systems used in electronics. We classify them by how many distinct symbols they use. That count is referred to as the ‘base’. DNA is a base-4 language (A,G,C,T), but it’s not a number system.
| Number system/ Language | Who speaks it | How many symbols (base) | Symbols |
|---|---|---|---|
| Decimal | humans | 10 (deci) | 0123456789 |
| Binary | computers | 2 (bi) | 01 |
| Octal | 8 (oct) | 01234567 | |
| Hexadecimal | 16 (hex + deci) | 0123456789 ABCDEF (10-11-12-13-14-16) |
You’d be amazed at how many gadgets send physical information to computers in some number language. But for our computer to manage and display it, the information must be converted to binary first.
Converting between number systems
In the magical way of math, converting these numbers from one system to another requires a simple formula that yields surprising, ironclad patterns. Believe it or not, the remainders of long division become your new number!
Using long division… Wait. There was a use for that after all? Now there’s a conversation starter. But I digress.
Using long division… Wait. Can’t I use a calculator? Go for it. Let me know how it goes.
Using long division, divide the number you want to convert by the base of the language you want it in, keeping the remainders, until you end up at 0 with a remainder. Write the remainders from bottom to top, and you have your number in the new language. Label the language by putting the base in parentheses as a subscript.
Sounds like something Harry Potter would say, huh? I’ll say it again, math is magical.
Try it yourself
I assume you are human and you count your age in decimal numbers because humans speak decimal. Let’s convert that to hexadecimal (base 16) so you can tell C-3PO when he asks your age.
If I remember correctly, you are 482 years old today.
Divide 482 by the new base (16), keeping the remainder.
Do it again.
Do it again.
Do it again.
Are we at zero plus remainder yet?
Now write the remainders from bottom to top. If any of them are over nine, covert them to their corresponding hex letter).
VOILA!
Click here to see if you got the right answer.
482/16 = 30 R2
30/16 = 1 R14
1/16 = 0 R1
Age in hexadecimal = 1-14-2 = 1E2(16)
Next time you C3PO, you can cheer him up by speaking his language. Except he’s probably unplugged and rusted at this point.