Binary Math

What is binary math?

The binary number system is a base-2 number system. This means it only has two numbers: 0 and 1. The word binary simply means “two”, for example, this is a binary star system because it has two stars orbiting each other:

binary stars

The number system that we normally use is the decimal number system. It has 10 numbers: 0 through 9.

Why use binary math?

Binary numbers are important if you want to understand how computers work. Digital electronics (like computers) are dumb but they can easily understand being “ON” or “OFF”.

In terms of electricity, the binary number 1 is a high voltage while the binary number 0 is a low voltage, or ground – which is just a fancy way of saying “ON” and “OFF”. So at a fundamental level, you could think of computers as machines for flipping binary digits on and off, kind of like a lamp – it’s either on (light) or off (dark).

This binary “on/off” language is the computer’s equivalent of our human language:


Everything you see or hear on the computer – words, pictures, videos and sounds – is made using only those zeros and ones. It’s hard to believe but it’s true!

Exercise: Counting In Binary

Here is a helpful table of the first 10 numbers to compare counting in decimal to counting in binary:

1 2 3 4 5 6 7 8 9 10
01 10 11 100 101 110 111 1000 1001 1010

Exercise: Cards

Make a couple sets of 5 cards like as shown below – just simple squares of paper with dots – and place them in the following order:


Q. Do you notice anything about the number of dots on each card?
A. Each card has twice as many dots as the card to the right.

Q. How many dots would there be on each card if we added two more cards to the left?
A. 32, 64

Q. In decimal math, if you add a zero to the end of a number, the number would be 10 times more. What happens in binary math?
A. The number doubles.

Now flip some of the cards face down, like this:


This is how we make binary numbers. The cards that are flipped down are zeros and the cards that are facing up are ones.

Q. If you count in binary, what number do you see if you flip the cards as shown above?
A. 9 (just count the dots!)

Q. How would you make the binary number “01001”?
A. Trick question! We already made a binary “01001” when we flipped the cards as shown above.

(Try flipping different cards to make different binary numbers. Hint: some numbers can be achieved using different combinations!)

Exercise: Faxes

Fax machines send and receive messages using the binary system too, by sending and receiving beeps. A high beep means a binary one and a low beep means a binary zero. Call any fax line right now and listen to it screech. It’s hard for our human ears to make out the high and the low beeps because they are being sent at high speeds but if you slowed the sound down, you would hear it.

Exercise: CDs and DVDs

CDs and DVDs use a binary system too, by having bits that reflect light and bits that do not (this is called optical storage). A shiny bit means a binary one and a matte bit means a binary zero. Go find a CD or a DVD and take a look at it under a light, turning it this way or that way. It’s hard for our human eyes to tell the shiny bits from the matte bits because they are so tiny but if you had a magnifying glass you would be able to see parts of the surface that reflect the light next to parts that don’t.

Bits and Bytes

Each of the cards we have used so far represents a “bit” on the computer – in fact “bit” is
just short for “binary digit“. In computer memory, the bits are made by a transistor that is switched on or off, or a capacitor that is charged or discharged.

One bit on its own is too small to be useful, so they are usually grouped together in groups of eight, which can represent numbers from 0 to 255. A group of eight bits is called a byte.

Take a break!

Breathe like this:


Text spam from 29 designs

Did you receive a spam text on your mobile phone from 29 Designs? The text message says “Final 1 hr Left to Activate your 70% Off Custom Animated Video Deal. Click Here to Activate Now & Grow your Sales by 1000%”. Here is the screenshot:

Spam text 29 designs - 1My number is on the national do-not-call registry and I have had no prior contact with this company so not only is this spam annoying, it is also illegal.

Their sales line is 619-942-5964 but of course no one wants to call a known spammer! The whois information is available but fake (address provided does not actually exist).

What can you do?

  • Report text to the FTC (1 minute form).
  • Report the company to ENOM (let them know about the spam and the fake registration information).
  • Email (their hosting company) and let them know that they are hosting a known spammer. Sample email:
    Hello, I received text spam from someone that hosts with you: My number is on the do-not-call registry and I have had no prior contact with this company. Their whois info is fake (for example address provided does not exist) and there are many people online complaining about the spam. Please let me know if you need any additional information.

Update #1

The spammer’s hosting provider A2 Hosting followed up on my complaint and took the offending website down! I am very impressed with their response – dealing with spammers is endless, thankless work that adds nothing to the company bottom line, so it really shows that A2 Hosting‘s actions are aligned with their official company values, which is a rarity these days.

Update #2

Shortly after the website was taken down (see Update #1 above), I received 2 more spam messages! The first message was similar to the original spam, reading “[Name], Final 1 hr Left to Activate your 70% Off Animated Video Deal. Click here to Activate Now & Grow your Sales”. Here is the screenshot, with my name removed (yes, it addressed me personally this time):

Spam text 29 designs - 2 - name removed

Unlike the original text which came from a short code,  this text came from an actual phone number 626-387-3785. Note the new, misspelled, domain; and the new sales line number 1-888-369-8031.

In addition to this message I got another text that read “Activate your Special Custom Logo Coupon! Click here to Get Your Logo for Only $29.”.

Not only these two texts popped up on my phone at the same time, the sales line for the new 29 Designs website is shared by a company called One Logo Design, a known SMS spammer with many reviews from people who paid them for logo design and never received any services. Curiously, the only positive reviews are from a single reviewer who gave 5 stars to a bunch of other spammy web design/development/video companies, including One Logo Design (sales like 1-888-369-8031), DesignVation (sales line 1-888-302-6534), and Video Cubix (sales line 1-888-374-1389). Company registration information is available for all of these companies but fake (address provided does not actually exist).

Spinach Pesto

Yields 1-2 cups. Prep time 10 minutes.


  • Two cups spinach
  • One cup fresh basil leaves
  • Half a cup raw pine nuts
  • One clove garlic
  • Quarter cup olive oil
  • Salt, to taste


Place all ingredients in a blender and pulse until very slightly chunky.

Store in an airtight container in the refrigerator for up to 5 days.

Zucchini And Watercress Soup

Serves 1. Prep time 10 minutes, cook time 20 minutes.


  • One zucchini, diced
  • Half a cup watercress
  • 1 stalk celery, diced
  • A handful raw cashews
  • Half an onion, diced
  • One cup vegetable or chicken stock
  • One tablespoon olive oil
  • Salt and pepper, to taste
  • Chopped fresh parsley, for garnish


Heat the oil in a soup pot over medium heat. Add onion and celery and sauté for 5 minutes, until translucent. Add the zucchini and sauté for another 3 minutes.

Add vegetable or chicken stock and cashews, and bring to a boil. Reduce heat to low, and simmer for 5 minutes (until the zucchini is tender). Add the watercress and cook for 3 more minutes.

Transfer to a blender (or use a hand-held blender directly in the pot), and blend until smooth.

Season with salt and pepper and garnish with chopped parsley

Serve warm or chilled.

Cauliflower Soup

Serves 1. Prep time 15 minutes, cook time 15 minutes.


  • Half a caulifower, cut into chunks
  • A handful of raw cashews
  • A quarter avocado
  • Half an onion, diced
  • One clove garlic, diced
  • One tablespoon tahini
  • One tablespoon olive oil
  • Salt and pepper, to taste
  • Chopped fresh parsley, for garnish


Heat the oil in a soup pot over medium heat. Add onion and garlic and sauté for 5 minutes, until translucent.

Add 1 cup water (preferrably distilled), caulifower, cashews, and tahini. Bring to a boil, reduce heat to low, and simmer for 10-15 minutes (until the caulifower is tender).

Transfer to a blender (or use a hand-held blender directly in the pot), add avocado, and blend until smooth.

Season with salt and pepper and garnish with chopped parsley.

Serve warm or chilled.