Math

$N_{(b)} = \sum_{i=-m}^{n-1} d_i \cdot b^i$

where $d_i$ is the digit at position $i$, and $b$ is the base.

Conversion from Decimal to Binary (Integer Part - Division Method):
To convert $(13)_{10}$:
$13 \div 2 = 6$ remainder $1$ (LSB)
$6 \div 2 = 3$ remainder $0$
$3 \div 2 = 1$ remainder $1$
$1 \div 2 = 0$ remainder $1$ (MSB)
Reading remainders from bottom up: $(1101)_2$.

• Injective (One-to-one): A function $f: A \to B$ is injective if $f(x_1) = f(x_2)$ implies $x_1 = x_2$ for all $x_1, x_2 \in A$. Graphically, this means any horizontal line intersects the graph at most once.
• Surjective (Onto): A function $f: A \to B$ is surjective if for every $y \in B$, there exists at least one $x \in A$ such that $f(x) = y$. Graphically, this means the range of $f$ is equal to its codomain.
• Bijective (One-to-one correspondence): A function is bijective if it is both injective and surjective. Bijective functions are precisely those that possess an inverse function.

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