Mathematics of cyclic redundancy checks
When you want to make sure that a message you send is not messed up or changed along the way, you use something called a "cyclic redundancy check" or CRC for short.
Imagine you want to send your friend a picture of a cat. You could just send the picture, but what if something happens during transmission and your friend receives a picture of a dog instead? That would be a problem!
So, what you do is add some extra numbers to the end of your message before you send it. These extra numbers are called "checksums."
The checksums are calculated by doing some fancy math on the message, but don't worry, we'll make it easy to understand.
First, we convert the message into a long string of binary digits (0s and 1s). Then we add some extra bits to the end of that string in order to make it evenly divisible by a specific number. That number is often called the "key" or "generator polynomial."
For example, let's say our key is "1001". We would add three zeros to the end of our binary string to make it divisible by 1001.
Then we do some more fancy math on the whole string - both the binary message and the extra zeros - to come up with a new binary number. This new binary number is our checksum.
When we send the message to our friend, we include both the original message and the checksum.
When our friend receives the message, they do the same calculations. They take the original message and add some extra zeros to the end so that it's evenly divisible by the same key (in our case, 1001). Then they do the same math we did to calculate the checksum.
If our friend's calculated checksum matches the checksum we sent, that means the message arrived safely and hasn't been changed. But if their calculated checksum doesn't match ours, that means something went wrong during transmission and we have to try sending the message again.
So, to sum it up: a cyclic redundancy check is a fancy math problem that helps you make sure the messages you send are not messed up or changed during transmission.
Imagine you want to send your friend a picture of a cat. You could just send the picture, but what if something happens during transmission and your friend receives a picture of a dog instead? That would be a problem!
So, what you do is add some extra numbers to the end of your message before you send it. These extra numbers are called "checksums."
The checksums are calculated by doing some fancy math on the message, but don't worry, we'll make it easy to understand.
First, we convert the message into a long string of binary digits (0s and 1s). Then we add some extra bits to the end of that string in order to make it evenly divisible by a specific number. That number is often called the "key" or "generator polynomial."
For example, let's say our key is "1001". We would add three zeros to the end of our binary string to make it divisible by 1001.
Then we do some more fancy math on the whole string - both the binary message and the extra zeros - to come up with a new binary number. This new binary number is our checksum.
When we send the message to our friend, we include both the original message and the checksum.
When our friend receives the message, they do the same calculations. They take the original message and add some extra zeros to the end so that it's evenly divisible by the same key (in our case, 1001). Then they do the same math we did to calculate the checksum.
If our friend's calculated checksum matches the checksum we sent, that means the message arrived safely and hasn't been changed. But if their calculated checksum doesn't match ours, that means something went wrong during transmission and we have to try sending the message again.
So, to sum it up: a cyclic redundancy check is a fancy math problem that helps you make sure the messages you send are not messed up or changed during transmission.
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