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When You Run Out Of Numbers

October 29, 2020

Have you ever considered how they name hurricanes? (Why they name hurricanes is a different question for a different post.) But, how are they named. We know they each have a name. Some are famous, Katrina, Andrew, Sandy. Others, are only names in the weather report.

The first Tropical Storm of the season is given a name starting with A. If it becomes a hurricane, the name is applied to the Hurricane. Andrew for example, was the first of the season. The second Tropical Storm is given a name starting with B, and so on. The names used to all be female. Now, they alternate male and female.

The alphobetical names continue on through letter Z. Names are reused in future years, unless a hurricane is particularly destructive. Then, the name is retired. There will never be another Hurricane Katrina, Camile or Andrew among others.

But, what happens when they run out of letters before we run out of tropical storms? Then, they start naming them using Greek letters. No clever names, just the names of the letters.

(So far)

I’m not sure what the plan is if we run through all the Greek letters. Considering there a 24 Greek letters in addition to the 26 English alphabet, means that there are 50 names possible. The most we’ve ever needed was 28. That was back in 2005.

We have a similar problem when counting. Everyone understands we have the numbers 0 to 9. But, what if you need to count higher than 9? Perhaps you think that next number is 10? And in our base-10 number system, you are correct. But, not always. I’ll explain how the next number after 9 is A. Followed by B, C, D, E and F.

Computers are stupid. Perhaps in a general sense of “Why can’t this stupid computer work.” But, also at their heart. Computers understand exactly two numbers: 0 and 1.

There are two types of people in the world.

1. Those who understand Binary

At their heart computers are a series of zeroes and ones. How do you count higher than 1 when the only optinos are a zero or a one? The same way you count higher than 9 in a decimal number system. You move to the next digit, 10. You do the same in a binary number system. You count by moving to the next place. In a base-ten number system we talk about digits. In a base 2, or binary system, we talk about the next bit.

I was introduced to binary counting in one of my first classes at college. The professor started with a question to the class,

Does anyone know sign language?

I do.

Then, you are the only person in class that can actually count manually.

I’m afraid I spoiled the professor’s example. He had members of the class stand in a row and using either an ‘up’ or ‘down’ hand, we learned to “count.” When the person next to you put their hand down, you raised the hand next to them. When, you raised one hand you lowered the other.

He was explaining the binary number system. Just as with decimal counting each place represents a power of ten, in a binary system, each place represents a power of two.

0 == 0
1 == 1
2 == 10
3 == 11
4 == 100
5 == 101
6 == 110
7 == 111
8 == 1000
9 == 1001
10 == 1010
11 == 1011
12 == 1100
13 == 1101
14 == 1110
15 == 1111
16 == 10000

In this way it’s possible to represent any number using just zeroes and ones. Inside your computer, your tablet, your phone, your network connected device. They all store information as a series of zeroes and ones.

As you look at binary representations, you migh notice something about the number 7 and 15. Each of them is represented by all ones. A base-8 number system is called an octal numeral system. A base-16 number system is called a hexidecimal numeral system.

With four bits using zeroes and ones we can express numbers from 0 – 15. As you can imagine it’s pretty challenging to read and write binary numbers. Very few people can look at the number 1101 and immediately think: 13. And larger number are even more difficult.

10110111? Well, that’s 183, of course. (I had to use a calculator to figure that out.) So, we came up with an easier way to “count” in binary. We use a base-16, or HEX system.

0 == 0
1 == 1
2 == 10
3 == 11
4 == 100
5 == 101
6 == 110
7 == 111
8 == 1000
9 == 1001
A == 1010
B == 1011
C == 1100
D == 1101
E == 1110
F == 1111

And when we get to 1111 and add one more that takes us to 1 0000. In our HEX system, we move to the next order of magnitude: 10h. The 1 represents 16. In this way we can continue to count in binary without needed to list out countless zeroes and ones.

To make things easier we break up the binary numbers into groups of 4. So, the binary number 10110111? We woudl express it as 1011 0111. Assiging a Hex number to each group of four digits, we can express 1011 011 as B (1011) 7 (0111), B7.

This conversion easily goes both ways, of course. If I have a Hex number A5, I can easily convert that to a binary number A (1010) 5 (0101) or 1010 0101.

Yesterday I talked about something called a MAC address. Every network aware device has a unique identifyer that is expressed as six hexidecimal numbers. A4:E9:75:4B:10:3C.

We know can easily convert this to its binary equivalent

A4 == 1010 0100
E9 == 1110 1001
75 == 0111 0101
4B == 0100 1011
10 == 0001 0000
3C == 0011 1100

A4:E9:75:4B:10:3C is 1010 0100 1110 1001 0111 0101 0100 1011 0001 0000 0011 1100.

It should be clear why it’s more efficient to use a hexidecimal representation for large binary numbers. Hopefully it’s also clear why multiples of 2 are so important. I remember 8 bit computers. Today, most computers are 64bit. Meaning they can recognize memory locations up to 64 bit’s long. That’s

0000 0000 0000 0000 0000 0000 0000 0000 or FFFF FFFF. The Decimal equivalent is 4,294,967,295. We typically don’t round hexidecimal numbers. However, we often do with decimal numbers. This number is slightly larger than four billion. Or, four gigabits.

One of the consequences of working with binary and hexidecimal number systems is that IT geeks get very good at counting in the decimal equivalent of binary.

It’s not a very interesting party trick, but ask your IT friend how far they can count in binary off the top of their head.

10 Two
100 Four
1000 Eight
1 0000 Sixteen
10 0000 Thirty-two
100 0000 Sixty-four
1000 0000 One hundred twenty-eight
1 0000 0000 Two hundred fifty-six
10 0000 0000 Five hundred and twelve
100 0000 0000 One thousand and twenty-four
1000 0000 0000 Two thousand and fourty-eight
1 0000 0000 0000 Four thousand and ninety-six
10 0000 0000 0000 ??

Like I said, it’s not a very interesting party trick but it’s one of the few IT geeks know.
Stay safe

Rodney M Bliss is an author, columnist and IT Consultant. His blog updates every weekday. He lives in Pleasant Grove, UT with his lovely wife, thirteen children and grandchildren.

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