What Is Binary? A Kid-Friendly Introduction

Long before we step into a math classroom, we learn a counting system built on tens. We use our ten fingers to count objects. Then, when formal math begins, we see how our numbers grow into places of tens, hundreds, and thousands. 

However, our familiar base-10 system is not the only way to count. There is another system built using only two options, and it is called binary. Chances are you have heard of it whenever people talk about computers. 

Today, Mathnasium tutors will explain what binary is, how binary numbers work, and how computers use the binary system. 

What Is Binary? 

Binary is a number system, also called a base-2 system, that uses only two digits: 0 and 1.

The word binary comes from the Latin word binarius, meaning “consisting of two.” That name fits because the system uses just two digits.

At first, this is hard to picture. We are so used to our decimal, or base-10 system, where we build any number using ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Binary may use only two digits, but it can still represent any number. We'll show you how. 

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How Do Binary Numbers Work? 

Every number system uses place value. A digit’s value depends on where it appears in a number.

In the base-10 system we use every day, each place is worth 10 times the place to its right. Starting at the right, the places are ones, tens, hundreds, and thousands.

For example, in the number 3,245:

• 5 is in the ones place, so it means 5 ones.

• 4 is in the tens place, so it means 4 tens, or 40.

• 2 is in the hundreds place, so it means 2 hundreds, or 200.

• 3 is in the thousands place, so it means 3 thousands, or 3,000.

We can also show that through a simple place value chart:

Binary uses place value, too, but it is a base-2 system. That means each place is worth 2 times the place to its right, rather than 10 times as much. 

We begin on the right with the ones place. From there, each step doubles the value:

• Twos place: Worth 2 ones (2 x 1)

• Fours place: Worth 2 twos (2 x 2)

• Eights place: Worth 2 fours (2 x 4)

• Sixteens place: Worth 2 eights (2 x 8)

Keep doubling, and the pattern continues: 1, 2, 4, 8, 16, ...

Because binary uses only the digits 0 and 1, each place has just two choices:

• 0 means “do not use this place value.”

• 1 means “use this place value.”

Let’s use the binary places 8, 4, 2, and 1 to write the number 3.

We do not need 8 or 4, so those places show 0. We do need 2 and 1 because 2 + 1 = 3. 

If we read the 0s and 1s, this gives us 0011. Usually, we leave off extra zeros at the beginning, so we write:

3 = 11 in binary 

Now let’s try 4. We need one group of 4, but we do not need any 2s or 1s.

So: 4 = 100 in binary 

Shall we try a slightly bigger number? Say 11. 

To make 11, we need one group of 8, one group of 2, and one group of 1.

We use 8, 2, and 1 because 8 + 2 + 1 makes 11. We do not use 4, so that place shows 0.

Reading the digits from left to right gives us:

11 = 1011 in binary

Not so difficult, right?

How Do Computers Use Binary?

Computers use binary to understand information because their electronic parts easily tell the difference between two states: off and on. An electrical signal is either off or on, and binary has two matching digits:

• 0 can mean off.

• 1 can mean on.

This makes binary ideal for computers. It is much easier for a computer to work with two clear choices than ten different choices.

One 0 or 1 cannot say very much by itself. But when computers put many 0s and 1s together, they create patterns that carry information.

For example, when you press the letter A on a keyboard, the keyboard sends a pattern of 0s and 1s to the computer. The computer recognizes that pattern as the letter A and shows it on the screen.

When you press a button in a game, the computer uses another pattern to know what to do, like making a character jump.

Binary patterns can represent numbers, letters, pictures, sounds, and instructions. That is how computers turn simple signals into the information we use every day.

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Over to You: Can You Write These Base-Ten Numbers as Binary Ones?

Using the place value charts we showed you earlier, turn these base-ten numbers into binary ones:

1. 2

2. 5

3. 6

4. 9

At Mathnasium, we use personalized learning plans to help students master any math skill, including binary numbers. 

How Mathnasium Helps Students Build a Deep Understanding of Math

Mathnasium is a math-only learning center empowering K–12 students of all skill levels to excel in math. 

Whether students need help (re)building foundational skills, mastering specific concepts like binary numbers, or taking on advanced math topics, we teach for deep understanding. 

Behind everything we do is the Mathnasium Method™, our proprietary teaching approach designed around individual learning needs and styles.

Here’s how it works.

Each student begins with a diagnostic assessment that helps us understand their current skill level, knowledge gaps, goals, and how they think and feel about math. Using these insights, we create a learning plan customized to their needs.

Our specially trained tutors follow the plan closely and provide live, face-to-face instruction in a caring and fun group environment. We teach for understanding using natural, everyday language and a mix of verbal, visual, mental, tactile, and written techniques.

During sessions, we always allow students to work independently before joining them to check their thoughts and processes. When we do step in, we show them both the how and the why behind the answer. Over time, students gain their own problem-solving skills and critical thinking tools they can use in math and beyond. 

Fun is part of the approach, too. We use hands-on and game-based activities, rewards, and consistent encouragement to help students stay engaged as they practice number systems, spotting patterns, or other math skills.

The results? True, measurable progress:

• 94% of parents report an improvement in their child's math skills and understanding

• 93% of parents report their child's improved attitude toward math after attending Mathnasium

• 90% of students saw an improvement in their school grades

With over 1,100 learning centers across North America, there is likely a Mathnasium close to you.

For families in and near Gambrills, MD, Mathnasium of Gambrills is a trusted local resource with a proven record of building confident math thinkers.

Whatever your child needs in math, our local team is happy to help. Start by scheduling a free diagnostic assessment with our center. We will use it to understand their current math skills and create a personalized learning plan for math mastery. 

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Pssst! Check Your Answers Here

If you tried our quick binary number challenges, see how you did below:

Challenge 1: 2 = 10 in binary

Challenge 2: 5 = 101 in binary

Challenge 3: 6 = 110 in binary

Challenge 4: 9 = 1001 in binary