* $\displaystyle \text{mod}\left(Y,100\right)$ takes the last two digits of $\displaystyle Y$. For example, $\displaystyle \text{mod}\left(1984,100\right)=84$
* $\displaystyle g(x)\equiv {\left\lfloor \frac{x}{4}\right\rfloor}+x$
* Can simplify using Conway's method of subdividing years by 12 (see additional notes)
* $\displaystyle D$ is the date number
* $\displaystyle D_{D}$ is the Doomsday number for the particular month
* For months 1 (January), 2 (February), ..., and etc., $\displaystyle D_{D}$ is as follows:
1. 3 (4 for leap years)
2. 28 (29 for leap years)
3. 14 ($\displaystyle \pi$-day)
4. 4
5. 9
6. 6
7. 11
8. 8
9. 5
10. 10
11. 7
12. 12
* E.g: What day was August 15th, 1930?
*$$
\begin{align}
d &\equiv f\left( {\left\lfloor \frac{1930}{100}\right\rfloor} \right)+g(\text{mod}\left(Y,100\right))+\cancelto{ \cancelto{ 0 }{ 7 } }{ 15-8 }~\left(\text{mod }7\right) \\
&= \cancelto{ \cancelto{ 5 }{ 12 } }{ 3+9 }+0 \\
&= 5\rightarrow \text{Friday}
\end{align}