Hello, Can someone please help explain binaries and decimals in a more simplistic manner? Thank you, Joe

Hi Joseph, In terms of binary, I'd suggest checking out the message board posts on binary: https://teamtreehouse.com/community/topic:digital-literacy/q:binary

But in short summary, binary is a completely different way of looking at counting. We live our lives in something called "Base 10" (probably because we have 10 fingers and toes to count with). So things start with 1 and go to 10 (so we have 10 base values to work with). So, for reasons I don't understand, computers were programmed in base 2 counting (probably because it took up less memory is my guess on those old computers the size of buildings). So the computer only knows how to count from 0 to 1. So the computer we know and love today translates everything it does from binary (aka base 2) to what we want the computer to do. In short, binary is simply another way of counting. :-) The computer has to do more complicated math (exponents) to translate its way of counting into ours, no different from translating like Italian into Japanese.

I'm not sure what all you'd like to know about decimals, but they're something used in math to measure smaller amounts than whole numbers...in computer programs there's typically 2 number types: decimal and floating point. Both of them use a decimal place, but the decimal type only goes out to the hundredth's place (2 decimal places, and no more than that) and typically decimal type is used with money, so $99.99 would be a decimal. Floating point can have any number of decimals, like the mathematical function pi: 3.14159265 is an example of a floating point. I think they call it floating point because the amount of decimals can "float around" (or it can vary) just like a feather doesn't float to the ground in a straight line.

I'll give it a try! The first thing I'd say is don't worry if you don't get it at first, it took me a while to wrap my head around it too.

Do you remember when you were at school and you learn about reading long lines of numbers? I was taught like this:

1000's 100's 10's 1's

The number on the left is the number of 1000's, then 100's, then 10's, then 1's. You can apply a similar approach to binary.

First of all, remember that binary only understands 0's and 1's - you can think of 0 as being "off" and 1 as being "on". If a binary digit is 0 then the switch is "off" and the value in that column is 0. If the binary digit is 1 then the switch is "on" and the value in the column can be added to the total value:

Let's start with a 4 bit chain, just because it's small and easier to understand.

The first bit on the right represents 2 to the power of 0, which is 1. The next column over is 2 to the power of 1, which is 2. The next column is 2 to the power of 2, which is 4. The next column over is 2 to the power of 3, which is 8.

So it would look like this:

2^3 2^2 2^1 2^0 0 1 1 0 = 2^2(4) + 2^1 (2) = 6

Another way to think of this is the next column to the left is the next number you can't make with your existing bits. so if they're all turned on, how much does the sum of all the bits equal? The most you can make with 4 bits is 15. So the next bit you add would equal 16 (or 2^4). You can now make 16 by writing the binary word 10000.

I hope that makes some sense.

Here's a fun game using light bulbs to represent the bits that might help make things a bit more clear: http://cdn.cs50.net/2015/fall/psets/0/pset0/bulbs.html

Jennifer Nordell, Nekilof, Stephen Shine....Thank You :)

One link lead to another and I somehow stumbled upon the below explanation

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

So if you have a binary number like 00000111 you could think of it like:

off - off - off - off - off - on - on - on, then just take the numbers that are "on" and add them up.

So, 4 + 2 + 1 = 7

What I'm unable to wrap my head around is, how does one read/ interpret/ break down these (eg. 2^0, 2^4, 2^6) in 0's and 1's.

Sorry for being a real pain, but I can't seem to make myself understand this :(