Issue while creating the list of Examples

Question

I have created the list of examples similar to the list of figures using the package "float" and the list of examples section is appearing correctly.But, I am facing 2 issues in the example section:

1. I don't want the caption to appear below the example.
2. The output of the example section, the examples are appearing at the center of each page.(i.e., only one example is appearing in one page and that too in the center of the page)

Packages and the float definition that are included before \begin{document}:

\documentclass[12 pt, a4paper]{book}
\usepackage{multicol}
\usepackage{geometry}
\geometry{
           a4paper,
           total={170 mm,257 mm},
           left=20 mm,
           top=20 mm,
          }
\usepackage{amsmath,bm}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{soul}
\usepackage{indentfirst}
\usepackage[utf8]{inputenc}
\usepackage{palatino}
\usepackage[dvipsnames]{xcolor}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{array}
\usepackage{enumitem}
\usepackage{mathtools}
\usepackage{cancel}
\usepackage{arydshln}
\usepackage{calc}
\usepackage{float}
\setlength{\parindent}{2em}
\newcommand{\wt}[2]{\underset{\substack{\textstyle\uparrow\\hidewidth\mathstrut#2\hidewidth}}{#1}}
\definecolor{mygray}{gray}{0.6}
\floatstyle{plain}
\newfloat{example}{tbp}{loc}[chapter]
\floatname{example}{Example}

Code snippet of Example section:

%% xxx---Example-1.1 Begins
\begin{example}
$\Longrightarrow$ \hspace{0.2 cm}\textbf{Example-1.1 :} \hspace{0.5 cm} \textit{Convert \hspace{0.1 cm}$(23.71)_{10}$ \hspace{0.05 cm}to its binary equivalent.}\\
\textbf{Solution :} \
\indent \textbf{Step 1 :} \hspace{0.2 cm} Separate the integer and the fractional part. \[0.1 cm]
\indent\indent\indent\indent Integer part: 23 \[0.1 cm]
\indent\indent\indent\indent Fractional part: 0.71
\indent \textbf{Step 2 :} \hspace{0.2 cm} Find the binary equivalent of the integer part.
    [\setlength\extrarowheight{2pt}
    \left.
    \hspace{-2 cm}

    \begin{array}{c|c|c}
        \textbf{Radix} & \textbf{Integer} & \textbf{Remainder}\
        \hline
         2 & 23 & 1\
        \hline
         2 & 11 & 1\
        \hline
         2 & 5 & 1\
        \hline
         2 & 2 & 0\
        \hline
         2 & 1 & 1\
        \hline
           & 0 &  \
    \end{array}
    \hspace{1 cm} \right\uparrow^{\textbf{LSB}}_{\textbf{MSB}} \
    ]
\indent \textbf{Step 3 :} \hspace{0.2 cm} Find the binary equivalent of the fractional part.
    [
    \left.
    \begin{array}{ccccc|c}
        \textbf{Fraction} & & \textbf{Radix} & & \textbf{Product} \hspace{0.1 cm} & \hspace{0.1 cm}\textbf{Integer}\
        0.71 & \times & 2 & = & 1.42 & 1\
        0.42 & \times & 2 & = & 0.84 & 0\
        0.84 & \times & 2 & = & 1.68 & 1\
        0.68 & \times & 2 & = & 1.36 & 1\
        0.36 & \times & 2 & = & 0.72 & 0\
    \end{array}
    \hspace{1 cm} \right\downarrow^{\textbf{LSB}}{\textbf{MSB}} \
    ]
\begin{flushright}
    \underline{Ans}. $\Rightarrow$ \fboxrule=1pt \fcolorbox{black}{mygray}{Binary Equivalent of $(23.71){10}$ = $(10111.10110)_{2}$} \[0.5 cm]
\end{flushright}
\caption[Decimal to Binary Conversion]{}
\label{example}
\end{example}
%% Example-1.1 Ends---xxx

The output of example section before inserting the code for list of examples:

The output of example section after inserting the code for list of examples:

Can anyone help me to do this? Also, if there is some better way of implementing list of examples other then the float package which can match my requirements. Please, let me know!!!

Answer 1

I minimized your MWE a bit more.

Note: The caption title does not have to be in braces, although if you look at the aux file, that is the default.

\documentclass{book}
\usepackage{float}
\floatstyle{plain}
\newfloat{example}{tbp}{loc}[chapter]
\floatname{example}{Example}
\begin{document}
\listof{example}{List of Examples}
\begin{example}
\caption{normal caption}
First example
\end{example}
\begin{example}
\refstepcounter{example}%
\addcontentsline{loc}{example}{\string\numberline{\theexample}{Invisible caption}}%
Second example.
\end{example}
\end{document}