Binary Numbers: What the World Counts On

The world has a natural perception of numbers. Numbers give us a way to describe, measure, and organize how we live our lives. Yet few would say that numbers themselves have been the underlying force that drives modern life. That has changed—knowingly or not.

As computers have become an integral part of our daily existence, we constantly encounter the idea of 1s and 0s. We hear about them, see them referenced, and depend on them every day. But do we really understand what they mean? How much impact do these 1s and 0s have on what we do? What are they, really?

We are comfortable counting in groups of ten. If we can connect that familiar idea of decimal numbers to binary numbers—numbers made up only of 1s and 0s—we can develop a much clearer understanding of the world that now surrounds us.

Why do we count by tens? Why does decimal feel natural, while other systems—dozens, ounces and pounds, feet, yards, and miles—feel less intuitive?

The reason is simple: we have ten fingers.

From the earliest times, people counted using their fingers. Each object counted corresponded to one finger. When all ten fingers were used and counting needed to continue, someone else was asked to hold up a finger to keep track of how many groups of ten had already been counted.

That person effectively became the tens holder. Each finger they raised represented another full group of ten. This freed the original counter to begin counting individual items again.

Counting using fingers — Using fingers to track groups of ten

Eventually, we developed an ingenious way to write this process down on paper.

We created ten symbols—0 through 9—to represent the count in a single column. This became the ones column. When that column reached its limit and one more item needed to be counted, we placed a 1 in a second column to the left. That column represented tens.

Each column holds a value ten times greater than the column to its right.

Decimal place value system — Each column increases by a factor of ten

Now imagine a person who has only two fingers. That person lives in a world where everyone has only two fingers.

Each column now holds twice the value of the column to its right instead of ten times.

Binary place value system — Binary system where each column doubles in value

The world of computers is that two-finger world.

Computers are built from tiny electronic components called transistors. Each transistor can represent only one of two states: ON or OFF.

Transistor ON and OFF states — Transistor states: ON (1) and OFF (0)

Because of this, computers naturally work with binary numbers—numbers made up of only 1s and 0s.

Everything a computer does relies on these binary numbers. Software, documents, images, music, and videos are all collections of binary values.

It is not necessary for every user to understand the technical details of binary numbers. The key point is simply this: only binary numbers exist beneath the surface. Everything else is interpretation.

It is remarkable that all the complexity of the modern world—from simple drawings to cars, airplanes, and global communication—depends entirely on combinations of tiny bits, each representing a simple choice between 0 and 1.