Tech Tips Home
The Best Tech Tips And Daily Deals
Newsletter On The Internet!

WorldStart Tech Tip And Store Search
Email: Password: Login Remember Me

Like what you see here? Subscribe to the Tech Tips newsletter!   Email: Subscribe

A Math Lesson: Binary System

Tuesday, July 1st, 2014 by | Filed Under: Computer Terms, I've Always Wanted To Know...

Have you ever noticed that certain numbers pop up over and over again in computers? Numbers like 32, 256, 512, and 1024 are commonplace, but why not just 30, 250, 500, or 1000? Why is it a 32 GB flash drive instead of a 30?  It is because computers calculate and compute using the binary system.

We have all learned to count using the decimal system. That means we have 10 numerals (deci meaning ten) to use, 0-9. However, computers use a different system called binary. This uses only two numerals – 0 and 1. Everything that a computer processes: words, letters, colors, pictures, is converted to those two numbers through switches on a computer chip. In actuality, to a computer this means “off” (0) or “on” (1). The computer either recognizes a signal or not. This is the reason computers were designed to work with the binary system. We don’t have any way to have a switch “halfway on.”

Unless you are really deep into programming or computer security, you will likely never need any skill in using binary numbers. Once you get into it, though, binary can be kind of fun. However, it does require a different way of thinking, and some simple math skills. I enjoy it because it is a challenge to my brain to think differently.

Here is an example of a binary number:


To figure out the decimal equivalent, let me explain the system a bit.

Similar to the decimal system, binary gets larger as you move to the left. But instead of multiplying by tens for each digit, you multiply by twos. Think about how the decimal system is set up. First you have the ones, then 1X10 is the tens, then 10X10 is the hundreds. Binary is the same, except you have ones, then 1X2 is 2, then 2X2 is 4 and so on. Here is a chart for my example.











Remember, if there is a 1, the “switch” is on, and if there is a 0, the “switch” is off. So if there is a one in the box, we add the numbers together. Adding all the ones together you get… (drum roll please)  19! (16+0+0+2+1)

You can extend the digits out as far as you need, each time multiplying the previous number by 2. After 16, you’d have the following values: 32, 64, 128, 256, 512, 1024. These values all pop up over and over in computing, especially in the past when we had smaller values of products like memory cards and flash drives. (When I was in grad school in 2005, I got a 256 MB flash drive to save my work, for free! Wow!)

You can also take a decimal number and convert it to binary. For example let’s start with 55. You would need to look at your binary values (1,2,4,8,16,32,64, etc) and find the largest one that would go into the number. In this case, 32. Place a 1 in that value. Then find the difference between the numbers, which is 23. Then repeat the process, placing a “1” in the place of each value, until you get to 0. I.E. 23-16=7, (do not need 8, so put a 0 in that value), 7-4=3, 3-2=1


There you have it, an introduction to the binary system. And now maybe you will better understand the geeky saying “There are only 10 types of people in the world: Those who understand binary and those who don’t.”

– Audra






5 Responses to “A Math Lesson: Binary System”

  1. Barbara Pickett says:

    Wow…whether my need to know appetite…and tempting me to get my toes wet…but alas I will probably never do it due to time constraints and old age…LOL keep up the good work.

  2. Barbara Pickett says:

    …duh.Ms Kindle choosing my words for me…you know I meant whetted don’t you???

  3. MarkJ says:

    I used to teach an introduction to computers class at our local community college. I assumed that everyone in there was like me and had been taught the idea of different numbers systems in school. I mean like middle school or at least high school but no they had no idea what I was talking about when I said decimal number system, octal, hexadecimal, duo-decimal etc. The concept just wasn’t there at all.

    So I attempted to teach them the same stuff you just went through. When I turned around I had a class full of blank stares. All of them still had no idea what was going on.

    I never tried to teach binary again.

    • James says:

      I just have to ask, did you try teaching them the ‘Dewey Decimal System’? Maybe library’s are just not ‘kool’, do kids still say that? Thanks for listening. James

Leave a Reply

Like these tips? Get them for FREE in your email!

WorldStart's Tech Tips Newsletter

  • Tech Tips Daily - Become a tech pro! Get the very best tech and computer help sent directly to your email every weekday!

  • Tech Tips Weekly - If you don't want our Tech Tips newsletter every day, then sign up for this weekly newsletter to get the best information of the week. Sent on Fridays.

Other Newsletters

  • WorldStart's Daily Deals - Every week, we send out great deals in our Daily Deals newsletter. Many of these deals are exclusively for our Daily Deals newsletter subscribers and can't be found with our regular specials.

  • Just For Grins - Each issue includes a couple clean jokes, some funny quotes, and a hilarious reader's story. Newsletter is sent five days a week.

Enter Email Address:


Your e-mail address is safe with us!
We only use it to send you the newsletters you request. It is NEVER disclosed to a third party for any reason, ever! Plus, if you decided you don't like our newsletters (don't worry, you'll love them), unsubscribing is fast and easy.

Free Newsletter Signup

Tech Tips Daily

Become a tech pro! Get the very best tech and computer help sent directly to your email every weekday!

Tech Tips Weekly

The week's best in tech and computer help. Get your issue sent to your email every Friday!

WorldStart's Daily Deals

The very best deals on the Internet! Get a new set of incredible sales every day of the week!

Just For Grins

Clean jokes, funny quotes, and hilarious comics. Sent 5 times a week straight to your email.


Love Worldstart? Refer A Friend!

WorldStart's Premium Membership

Tip Archive