Easy Way to Count in Binary! 1's and 0's

Have you every wanted to count like a computer, or just wondered how computers count this is the instructable for you!

First we need a little information of binary. Computers have 2 numbers in there system except there not numbers there switches. 1 meaning "ON" (like a light bulb) or 0 meaning "OFF"

So...

10110011

would be...

On, off, on, on, off, off, on, on

Then the computer interprets that into its numbering system, which later may convert it into ASCII. Correct 8-bit binary only has 8 digits. There are 16, 32, 64, and 128 bit processors that take more numbers than just 8 at a time. This tutorial is for 8-bit.

Materials:
Paper and Pencil
(optional) Genius to help

Step 1: Preparing

On the paper write this on the top.

This is the 8-bit binary cheat sheet. Column 8 (the one all the way to the right) is 1, column 7 is just a double of the earlier column, etc.

"Binary Cheat Sheet:

128 - 64 - 32 - 16 - 8 - 4 - 2 - 1"

and pick a number between 1 and 255

My number is 175

Step 2: Analyze the Number

Analyzing your number is very easy, here how it works.

Get your paper and right down your number under your Cheat Sheet.

First does the first number (128) fit in your number? The reason you check this, is because it helps you know if it is a 1 or a 0. Which makes up your number.

128 fits 175

If so subtract your number by the number you checked, then repeat for the rest of the numbers. Also if it did fit that means its a 1 and if it doesn't its a zero. This prepares the number for the next digit in the binary number.

so I'll start over...

175 - 128 = 47 *it fits so its a one* (1 _ _ _ _ _ _ _)

47 - 64 = -17 *Invalid so its a zero* (10 _ _ _ _ _ _)

47 - 32 = 15 *it fits so its a one* (101 _ _ _ _ _)

15 - 16 = -1 *Invalid so its a zero* (1010 _ _ _ _)

15 - 8 = 7 *it fits so its a one* (10101 _ _ _)

7 - 4 = 3 *it fits so its a one* (101011 _ _)

3 - 2 = 1 *it fits so its a one* (1010111 _)

1 - 1 = 0 *it fits so its a one* (10101111)

If you didn't get zero you did something wrong and go back and check your work.

Step 3: There Is Your Binary Number!

If you did everything correctly, you should have a 8 digit number. Like so, 10101111.

Thanks for reading my instructable.

Comments

[drea1076]

Wowzer!!! Thank you for making this so simple and easy to understand. I am very grateful for you taking the time out to provide a set of clear instructions on this binary counting technique. I have a sense of hope that I can complete my quiz with a passing grade now. On a different note, I like the swamp cooler idea too.

[Jinu18]

Upto how much values this idea can be used. Making it simple how will I calculate a value like 900

[SiroBaba]

Easy:
Solve with 10bit binary cheat sheet, which can accommodate any number between 1 to 1,023.
Your answer will be 1110000100.

[zachc1]

you would need to display this binary code aprox. 11 times (10.58 to be exact) "01010101"

[knighthawke2k]

Nicely done! This is something that those of us working with networking use to convert ip addresses. Your cheat sheet is very useful in explaining a quick method of getting to the binary number and people can use your sheet to study when taking the network + certification test. Thank you for taking time to put it together. Good job!!

[leighbrody]

why choose a number between 1 and 255? What's the significance of 255?

[Sparsh Goyal]

Hey is this functional with 12

[TallGlassOfMike]

"First we need a little information of binary. Computers have 2 numbers in there system except there not numbers there switches."

SHOULD BE

"First we need a little information of binary. Computers have 2 numbers in THEIR system except THEY'RE not numbers THEY'RE switches."

[karimh9]

Very simple way of converting decimal number to a binary digit.

175 /2 = 87 ignore the r.
87/2= 43 ignore the r
43/2 = 21. Ignore the r
21/2= 10. ............... r
10/2=5. ................ r
5/2 =2. .................. r
2/2=1. ...................r that’s it that the end. The sequence you have look like this :
1-2-5-10-21-43-87-175
Under each odd number you put 1
and under each even number you 0

The binary digit of 175 is 10101111

Thank you

[MubasharA1]

Thanks a lot for wonderful and very easy way to decode and encode binary number.

[TristonW]

10101111? would that be the answer? Im really trying to understand this lol

[mwilliams937]

Thank you so, so much. I have been trying to figure this out for some time now. No one, and I mean no one was able to get me to understand how to do this. I got on your site for the first time and now I got it. Please keep me informed as I will be using your site for future help.

God Bless you all.

Martin L. Williams

[nutsandbolts_64]

8-bit eh? You may have noticed this:
_______________________
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
----------------------------------------
128 = 2 to the 7th power
64   = 2 to the 6th power
32   = 2 to the 5 th power
etc...

Use that ASCII chart up there for reference.

[alltootechnical]

LOL! I can count base 3, 4, 8, 101 Can you show a tutorial for counting in other bases ?

[Pentacle]

VERY cool.

[Geeko]

Thanks for the input's I updated my instructable upon your feedback. I hope to find this helpful to some people! (-_- Lemonie!)

[lemonie]

Binary isn't much (or any?) use to most people, you might do well to instruct on hexadecimal instead? L

[PKM]

Oh and correct binary only has 8 digits.

As karossii says, you are thinking of a byte. I'm sure your 32 or 64 bit computer CPU deals with numbers over 8 bits.

Your method is sound and quite straightforward but it sounds like you rushed the core part a little bit- you compress all of the instructions on how to actually convert a number into

Get your paper and right down your number under your Cheat Sheet.
First does the first number (128) fit in your number?
...
If so subtract your number by the number you checked, then repeat for the rest of the numbers. Also if it did fit that means its a 1 and if it doesn't its a zero.

That last part could do with taking a breath and explaining what you are doing a little bit more clearly. Otherwise, good work.

[jaidex]

Nicely done! I've tried to explain binary to people for years, but I've never taken the time to stop and THINK about it - next time I need to explain it, I'll use your method!

[karossii]

As a side not, binary numeral systems date back to BC days, I believe documented back to about 800BC or so if memory serves, and used as many (or few) digits as needed for the number to be represented; and the (similarly dated BC) Chinese binary systems used 3 digit and 6 digit groupings for their binary numbers. bits/bytes or binary octets (another term for using 8 binary digits) are a result of the computer age (as far as I know - I could be mistaken).