Bits and Bytes, It's all Done By Code
A computer processes information by turning electricity on and off. It is amazing that everything a computer does is grounded in either the presence or absence of extremely small amounts of electricity. On or off. That's it. Now, you might say that this sounds daft, that your word processor, spreadsheet, or internet browser program, cannot possibly work because of little charges turning on and off like Christmas lights. But in fact that is true. Those little charges, like little acorns, grow indeed to be big things.
We can do quite a bit by turning electricity on and off. Morse code, that system of dots and dashes, uses short or long electrical bursts to represent letters and numbers. International Morse code represents the letter "A" with a dot, electricity turned on for a small amount of time, a space, electricity absent for a short amount of time, and a dash, a longer electrical burst than the dot. Different combinations of dots and dashes stand for other letters. Good telegraphers can send fifty words or more per minute using Morse code. Teletype machines sent information even faster using the Baudot code. All done by turning electricity on and off.

With computers we use a different kind of code, the most common being something called ASCII, which stands for, hold your breath, the American National Standard Code for Information Interchange. Of course. Eight parts make up all ASCII characters, each part called a bit. A bit can be a charge of electricity or a lack of electricity. That's a big difference than Morse Code.
With Morse different characters like A, B, or C, are made up of differing amounts. Three parts make up the letter A like we showed above, while the letter V is made up of seven parts: dot, space, dot, space, dot, space, dash. In ASCII all characters make up the same amount, eight bits which we call a byte. Also, Morse code has three states: electricity on for a short amount of time, electricity on for a longer amount of time, and, of course, electricity off. With ASCII we have two states, a binary code; electricity only on or off. Which works out fine.
When you punch in "A" or "B' on your computer keyboard a microprocessor doesn't recognize those letters as such, instead it responds to 0s and 1s, bits, pulses which make up a byte. Bits and bytes are the building blocks of digital.
You're probably wondering how all these 0s and 1s stay together and not get lost. That's a big concern -- we must be sure that what we sent is what got across. A bank wouldn't want their automated teller machine to hand out a thousand dollars when only a hundred was intended. So what do we do? We add a bit to our code and use a simple routine to automatically check our byte or digital character.
The extra bit we is called the parity bit, the watch guard for the letter. A newer, better method exists to check data integrity, known as a cyclic redundancy check. Let's look at bit parity checking instead, since you'll find so many references to it. It is elegantly simple but difficult to grasp on the first read. Here's Jade Clayton's presentation, from his excellent McGraw Hill Illustrated Telecom Dictionary. Read it once or twice and you will get it:
"Bit Parity: A way to check that transmitted data is not corrupted or distorted during transmission. . . Take a bit stream that will be transmitted, add all the bits as binary numbers mathematically, and the resulting number is odd or even. Add a 1 at the end of the stream if the number is even and a 0 if the number is odd.
When the bits are received at the other end, they are added up and compared to the last bit. If they add up to be an even number, then the last bit should be a 1. If they add up to be an odd number they should be a 0. If the case for either does not hold true, the receiving end sends a request to retransmit the stream of bits. They are retransmitted, with the parity bit attached all over again.
For example, a computer sends a bit stream of 10101011. Simply adding the bits gives a sum of 1+0+1+0+1+0+1+1=5. This is an odd number so add a 0 to the end of the stream to make it 101010110. The bits are received at the other end, added together, and compared to the parity bit the same way. There are new and more sophisticated ways of checking for errors in data transmission, such as cyclic redundancy checking." Jade Clayton, writing in the McGraw Hill Telecom Dictionary
Get it? Parity check adds or sums the bits in a byte. If it is an odd number a 0 is tacked onto the end of the group and if it is an even number a 1 gets put on. Once received, Mr. Computer adds up the original eight bits. It then looks at the parity bit, to see if it agrees with the sum. If not, retransmit and try again!
A related link is here, to a packet and switching discussion. (internal link)