OneO1

"...show the count..."
"...in this way..."

If I just do 'short line' 'long line' for each number based on it's digit value and assign zero to 'short' and one to 'long', then we get this:

7.4.13
long, short, long
1 0 1

101 binary = 5 Hex, 5 Oct, 5 Decimal and as Decimal 5, it then is E in Alphabet.
Source: Me at the Windows calculator toggling between the settings to see which is what.


"How then could we make a code that can correct errors? One simple example is to repeat the message three times." ***

I put 101 'next' to itself three times...

101101101 in binary = 365 in decimal. Like 365 days a year maybe? Co-ink-e-dink!~

"...show the count of the 7, 4 and 13. In this way..." ***

7 x 4 x 13 = 364 (3+6+4) = 13

101101100 bin = 364 decimal.
101101101 bin = 365 decimal.

This is a pair.

Definitions of Error detection and error correction:
Error detection is the ability to detect the presence of errors caused by noise or other impairments during transmission from the transmitter to the receiver. Error correction is the additional ability to reconstruct the original, error-free data....

A parity bit is an error detection mechanism that can only detect an odd number of errors.

The stream of data is broken up into blocks of bits, and the number of 1 bits is counted. Then, a "parity bit" is set (or cleared) if the number of one bits is odd (or even). (This scheme is called even parity; odd parity can also be used.) If the tested blocks overlap, then the parity bits can be used to isolate the error, and even correct it if the error affects a single bit: this is the principle behind the Hamming code.

There is a limitation to parity schemes. A parity bit is only guaranteed to detect an odd number of bit errors (one, three, five, and so on). If an even number of bits (two, four, six and so on) are flipped, the parity bit appears to be correct, even though the data is corrupt.


Checksum A checksum of a message is an arithmetic sum of message code words of a certain word length, for example byte values, and their carry value. The sum is negated by means of ones-complement, and stored or transferred as an extra code word extending the message.

On the receiver side, a new checksum may be calculated, from the extended message. If the new checksum is not 0, error is detected.

Checksum schemes include parity bits, check digits, and longitudinal redundancy check.
Source: Wiki