Why 255 bits

I know 2, 4, 8, 16, 32, 64, , , , , , , , , etc.. Yes we're a strange bunch. Now that we know about the binary values in a computer, let's talk about the devices which use these values. At the heart of all binary computers is the AND-gate. This is a little electronic switch or valve if you'd like consists of two inputs and a single output and is usually implemented with a transistor.

According to the definition, if and only if both of the inputs to an AND-gate are "on" then the output is "on". Otherwise, if either one of the inputs is "off" or if both inputs are "off" then the output is "off". It's certainly not that easy however the point is that the AND gate, the basic building block of a computer, takes 2 inputs to get an output.

At some point, the early designers of the binary computer came up with the byte as the next standard unit above a bit. A byte is defined as 8-bits and can represent values from 0 to , or 2 to the power of 8 different values.

Repeat the process until the quotient becomes 0. Step 2: Write the remainder from bottom to top i. This will give the binary equivalent of To find decimal to binary equivalent, divide successively by 2 until the quotient becomes 0.

The binary equivalent can be obtained by writing the remainder in each division step from the bottom to the top. We know that in binary is and 9 is We can count the number of zeros and ones to see how many bits are used to represent in binary i. Therefore, we have used 8 bits to represent in binary. This makes it really easy to encode and decode. This Left shifts the 8 bits of the first byte 8 positions to the left.

This is a Bitwise AND. Used this way the right side of the expression will act as a mask to zero out one byte so we can work with just the other one.

If the range of expected values is bigger than we can use the same trick. The only difference is that we have to manually shift bits when we encode on Arduino, just like we did in the payload function.

To tell the difference between and you will need a signed data type. This does mean that for example in a word only 15 of the 16 bits are available for the actual number, limiting the range from to The data types we used so far are all signed, which means all of the tricks work just as well for negative values.

Just be aware of the maximum value. So far we have only dealt with rounded numbers. What if you need more precision?

The answer very similar to how we indexed or rounded big numbers. Simply multiple and divide the value as you encode and decode it. Note that it uses Start off by encoding each individual number to a buffer of bytes and then combine them into a single buffer.

Think of it as an instruction to copy to the payload buffer, but after moving the point it will copy to, with the length of the payloads we added so far.