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

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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

Teacher Notes

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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.

18 Discussions

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

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

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.

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).

one comment - 'correct' binary is simply a base2 system of counting, and has anywhere from 1 digit to as many as are needed. That would be like trying to say correct decimal has 9 digits (or 5 digits or 12 digits, etc.). What you are referring to is a binary 'byte' which has 8 'bits' of data... t ues the binary system, but it is not the binary system. For example, this is a perfectly proper binary number; 1110010100101, which equates to 4096+2048+1024+128+32+4+1 or 7,333 in decimal. And this is (outside of a computer) a stupid way to write a binary number; 00000011. That equates to 3 in decimal, but would be like writing out "0000003" - why waste 6 leading zeros for nothing? Your instructable is partially correct, but also very misleading. You should either rename it and clarify that you are instructing on bits/bytes of data, or remove the 8 digit qualification you reference throughout.