Looking to add a little math to your art lesson? We’ve got you covered!

In this activity, we will explore the binary number system and learn how to use division to convert decimal numbers into binary sequences – and awesome pieces of art.

First, though, a little lesson in bits and bytes:

Computers don’t understand numbers, pictures or letters the way we do. For them, data is stored and transmitted as a series of 0s and 1s in what is called a binary system. The binary system is “binary” because it uses only two digits to represent information: 0 or 1.

The binary number system is made up of bits, and a sequence of eight bits make a byte. A bit alone cannot relay much information, so they are usually grouped into bytes, which can represent numbers from 0 to 255. Binary code is stored onto a computer as character sets known as ASCII (as-kee), which stands for American Standard Code for Information Exchange. ASCII is used as a character encoding standard for electronic communication.

Often, we hear about 64-bit or 32-bit computer processors. This number tells us the number of bits the computer can process at once, and thus, its speed. Nowadays, most computers are 64-bit, meaning they can process 64 bits of information in one process, whereas 32-bit computers would have to break down 64-bit information into smaller pieces before processing, making it a slower process.

Now that we have a basic understanding of the binary system, let’s learn how to decode decimal numbers into binary sequences and reveal which grid blocks are assigned which colors as we create fun art pieces.

This activity will take about five minutes of preparation and 30 minutes to an hour of learning time. It is best suited for students in grades 4-9.

While this can be a tricky process and may be difficult, it’s extremely rewarding and gratifying to learn something new and challenge your brain. Don’t be afraid to take a step back, think about the problem and keep trying. Learning binary code is really fun once you get the hang of it! Don’t give up!

Materials:

• Graph paper or worksheet grid (Find printable worksheet grids below)
• Crayons, colored pencils or markers
• Pencil
• Scrap paper (to write out division work)
• Calculator (to double check answers)

Directions:

Let’s start with Project 1. Print out or recreate the grid worksheet labeled “Project 1 Binary Blank Grid” (pictured above and available at the bottom of the blog.) The grid has 8 rows and 8 columns, with a number assigned to each row to decipher.

To perform the decimal-to-binary conversion we take each decimal number and divide by two until we get to 0. As we perform each division, a 0 is written down as the bit number if there was NO remainder in the result, and a 1 is the bit number if there IS a remainder, regardless of the remainder.

1. Divide your first number (top row) by 2.

a. After dividing, if the answer was a whole number, the binary bit is a 0.

b. If there was a remainder, the binary bit is a 1. Round down to the nearest whole number, this will be our next division number.

2. Divide the answer we got out of our first division by 2. Note its binary bit value of 0 or 1 using rules in step 1.

3. Continue division using this method until you reach the point where your division is 1÷2.

4. List your bits in order from last to first, this is to arrange it from Most Significant Digit to Least Significant Digit.

5. If you don’t have 8 bits, add 0s to the beginning of our sequence until we have 8 total bit numbers.

6. We have our first binary sequence! On the grid, write in your binary in each box of the first row. We can now color in our first row. 0s will be the first color, and 1s will be the second. Check out the work shown for our first row below.

Here’s what your work should look like:

• 60 divided by 2 = 30; (0, no remainder)
• 30 divided by 2 = 15; (0, no remainder)
• 15 divided by 2 = 7.5; (1, remainder present, round down to 7)
• 7 divided by 2 = 3.5; (1, remainder present, round down to 3)
• 3 divided by 2 = 1.5; (1, remainder present, round down to 1)
• 1 divided by 2 = .5; (1, remainder present, round down to 0)

Arranged from last to first: 111100
Added in 0s to make complete 8-bit byte: 00111100

7. Repeat steps 1-5 to decode the remaining rows, then color it in accordingly to reveal the art design!

8. Once you’ve completed Project 1, try out the other four projects we are sharing with you. Their grid sheets are below.

Looking for an even bigger challenge?

Use a blank grid to color in your own design. Make something that you like or something that someone else will like when they decipher the image.

Remember, binary only works with two values, so only use two colors in your design.

Once you have your design, work to convert your binary design into decimal numbers. This is done a little differently than what we’ve already done. This time, we will be working with Powers of Two. We only need the first 8 powers since we are working in 8-bit sequences.

This table will show us the Powers of Two we are using:

1. Write out the byte binary sequence for each of your rows, one color will be 0s, the other 1s.

2. For each byte sequence you will need to perform the following to convert your binary sequence to a decimal number:

NOTE: If a Bit is a 0, Power of Two number is skipped; if bit is a 1, Power of Two number is carried down.
EXAMPLE:

3. This decimal number now represents that entire row of binary bits! Repeat this for all 8 rows of your binary design.

4. Take all of your encoded decimals and arrange them to the left of their matching rows on an empty grid.

5. Share it with someone to decode using our original division method!

Still want more?
Check out our blog on creating secret messages with binary code!