## On numbers in computer science

**Author: Allison Figus**

We call our counting system DECIMAL. These are the numbers you see all over.

We, most of us, have 10 fingers. Mathematical Historians postulate that our decimal number system came about because

We, most of us, have 10 fingers. Mathematical Historians postulate that our decimal number system came about because

- We are often born with 10 fingers
- And we like to count on our hands

## DIGITS. what are they?

Fingers are sometimes called digits...

The digits of our

The digits from 0 to 9 are the numerical

Notice that ten (10) is not a digit. It is a combination of two digits: 1 followed by 0.

**DIGIT**sort of means*One of Ten*.The digits of our

*Decimal Counting System*are not new to you: 0, 1, 2, 3 ... 7, 8, 9. ("..." can be read as "and so on, until.")The digits from 0 to 9 are the numerical

**SYMBOLS**of the decimal counting system.Notice that ten (10) is not a digit. It is a combination of two digits: 1 followed by 0.

## base 10

Because our decimal number system has ten different symbols (the digits), we say that it is

This means that it has properties related to

*Base 10*.This means that it has properties related to

*Powers of 10*.**Powers**are also called**Exponents**.## Question 1

Let's start with an easy question. It's easy, but it gets at a concept that has

1,000,000 happens to be 10^6 (10 to the 6th). Powers of 10 are easy to compute:

**RAMIFICATIONS**you may never have thought of.**Q**What is the largest number you can represent with 6 digits?**A**999,999. One less than a million1,000,000 happens to be 10^6 (10 to the 6th). Powers of 10 are easy to compute:

**10^6 = 10 x 10 x 10 x 10 x 10 x 10**

= 1,000,000

= 1,000,000

So, with 6 digits, we can

**REPRESENT**one million numbers. (We can represent 0 to 999,999. Since 0 is a number, that is one million numbers).## question 2

**Q**What is the largest number you can represent with 6

*symbols*?

**A**Wait. What's the difference?

The answer is:

*it depends; on how many symbols you have to choose from*.

In our usual counting system,

*Base 10*, there are 10 symbols to choose from. But there are other counting systems; other bases! Computers, these days, use

*Base 2*, aka BINARY.

In

*Base 2*, you have only

*two*symbols to choose from: 0 and 1. The largest number you can represent in 6 binary symbols is

**31**.

## WISE GUYS

Once you fully learn this lesson, you'll know what this popular American joke means:

there are 10 types of people in this world: those who know binary and those who don't.