Centering a 64 bit-string comparison relative to the pages absolute center

Question

I'm using a table to show a comparison of two 64-bit blocks/strings — bit for bit.
Like so:

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Without the table it of course fits comfortably with room to spare, but when we draw the tables, extra space is added between each value on account of the minimum width of each cell. However, we can override this minimum width by putting \setlength{\tabcolsep}{1.0pt} between \begin{table} & \begin{tabular}. You can go all the way down to 0.0pt (probably even further if you really wanted to), and each cell gets its sides squished in. At 0.5pt, it will fit nicely between my 1.25in margins, but any bigger, it will be flush with the left margin, and overhanging the right.

I'd like to know how to get the table to ignore the margins and become truly centered, relative to the center of the current page. It shouldn't affect anything other than the table (surrounding text for instance). Just a quick temporary override. I thought it was possible with a minipage environment to get a float to.. well float, but I'm not having much luck.

Here's my MWE for the image above:

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\documentclass[a4]{article}
\usepackage{booktabs}
\usepackage{colortbl}
\usepackage{xcolor}
\usepackage[margin=1.25in,a4paper,showframe]{geometry}
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\makeatletter
\newcommand*{\yncellcolor}{}
\def\yncellcolor\ignorespaces{\@ifnextchar{1}{\cellcolor{green!20}}{\@ifnextchar{0}{\cellcolor{red!20}}{}}}
\newcolumntype{C}{>{\yncellcolor}c}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}\tiny
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}
\centering
\begin{center}
    \setlength{\tabcolsep}{1.0pt}
\begin{tabular}{|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|C|}

\hline
1 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 \\
\hline
0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 0 & 0 & 0 \\
\hline

\end{tabular}
\end{center}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
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Please, no obvious suggestions about font size, etc. Thanks.