A binary operation means that you are taking two things in and you are getting one thing out; for instance:

\begin{equation} f: (\mathbb{F},\mathbb{F}) \to \mathbb{F} \end{equation}

This is also closed, but binary operations doesn’t have to be.

A binomial distribution is a typo of distribution whose contents are:

• Binary
• Independent
• Fixed number
• Same probability: “That means: WITH REPLACEMENT”

Think: “what’s the probability of \(n\) coin flips getting \(k\) heads given the head’s probability is \(p\)”.

constituents

We write:

\begin{equation} X \sim Bin(n,p) \end{equation}

where, \(n\) is the number of trials, \(p\) is the probability of success on each trial.

requirements

Here is the probability mass function:

\begin{equation} P(X=k) = {n \choose k} p^{k}(1-p)^{n-k} \end{equation}

bioinformatics is a field of biology that deals with biology information. Blending CS, Data, Strategies and of course biology into one thing.

First, let’s review genetic information

possible use for bioinformatics

• Find the start/stop codons of known gene, and determine the gene and protein length

bitmasking is a very helpful to create bit vectors.

• | with a 1-mask is useful to turning things on
• & with a 0-mask is useful to turning things off (bitvector & not(1-mask))
• | is useful for set unions
• & is useful for intersections of bits
• ^ is useful for flipping isolated bits: 0 is bit preserving, 1 is bit negating
• ~ is useful for flipping all bits

& | ~ ^ << >>

&

Bitwise level AND

|

Bitwise level OR

~

Unary bitwise negation

^

Unary XOR

<<

Shift the number to the left. Fill unused slots with 0.

>>

Shift the number to the right

• for signed values, we perform an arithmetic right shift: fill the unused slots with the most significant bit from before (“fill with 1s”)
• for unsigned values, we perform a logical right shift