Hello. The purpose of this thread is to discuss the manipulation of sequences in base-two, or binary.
Naturally, all binary numbers are simply mathematical sequences starting from the 0th term such that s[t] = n * 2^t, assuming that "s" refers to the sequence, t refers to the term, and n refers to the actual value of the term.
Since binary only has the values of 0 and 1, it utilizes the exponents of two to calculate the value of each 0 and/or 1 in a positional manner.
An example sequence is "0101"
Since binary is read from a right-to-left manner, the sequence is equivalent to this:
(0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1).
As you may have noticed, the exponents of two are actually the term indices within the sequence. The exponents are also sequentially-successive.
The use of 0 and/or 1 is beneficial because it allows us to easily determine which values will be included within the series of the sequence, which is the base-ten equivalent of the binary number.
Hopefully this will elicit an interesting and wholesome discussion involving base-two manipulation. |