Issue with the alignment of the array

Question

I am having the issue with the alignment of an array.
Please, find the below code:
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}

setlength{parindent}{2em}

newcommand{wt}[2]{underset{substack{textstyleuparrowhidewidthmathstrut#2hidewidth}}{#1}}
definecolor{mygray}{gray}{0.6}

begin{document}
  textbf{Solution :}
    [
    left.
    hspace{1 cm}
    begin{array}{cccccc}
               &   & 1 & 0 & 1 & 0 
        times &   &   & 1 & 0 & 1 
        hline
               & underline{1} & 1 & 0 & 1 & 0 
               & 0 & 0 & 0 & 0 &   
             1 & 0 & 1 & 0 &   &   
        hline
             1 & 1 & 0 & 0 & 1 & 0 
    end{array}
    right. hspace{0.25 cm}vline hspace{0.1 cm} text{parbox[t]{13 cm}{As, the product of binary multiplication would always be less than 2. It won't generate any carry.}}
    begin{array}{ccccccccc}
        & & textbf{Product/Sum} & & textbf{Base} & & textbf{Carry} & & textbf{Result} 
        1 + 0 + 1 & = & 2 > 1 & = & 2 & times & 1 & + & 0 [0.2 cm]   
    end{array}
    ]
end{document}

The obtained output of this is as follows:

As, one can see in the image the second array is aligned to the right of the text. I want that array below the text.
The desired output is as follows:

Can anyone help me to solve this issue?

leandriis · Accepted Answer

Probably not too elegant since I used nested tabulars to position math elements, texts and lines.

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}

setlength{parindent}{2em}

newcommand{wt}[2]{underset{substack{textstyleuparrowhidewidthmathstrut#2hidewidth}}{#1}}
definecolor{mygray}{gray}{0.6}

usepackage{calc}

begin{document}
  textbf{Solution :}
  
begin{tabular}{p{0.25textwidth-2tabcolsep-arrayrulewidth}|p{0.75textwidth-2tabcolsep}}
        (begin{array}[t]{cccccc}
               &   & 1 & 0 & 1 & 0 
        times &   &   & 1 & 0 & 1 
        hline
               & underline{1} & 1 & 0 & 1 & 0 
               & 0 & 0 & 0 & 0 &   
             1 & 0 & 1 & 0 &   &   
        hline
             1 & 1 & 0 & 0 & 1 & 0 
    end{array})
    &
    begin{tabular}[t]{@{}p{0.75textwidth-2tabcolsep}@{}}
    As, the product of binary multiplication would always be less than 2. It won't generate any carry. 
    hdashline   
    [begin{array}{ccccccccc}
        & & textbf{Product/Sum} & & textbf{Base} & & textbf{Carry} & & textbf{Result} 
        1 + 0 + 1 & = & 2 > 1 & = & 2 & times & 1 & + & 0 [0.2 cm]   
    end{array}]
    end{tabular}
end{tabular}

end{document}

egreg · Answer

In order not to guess about the width of the material on the right side, you can use tabularx and nest array and tabular in it.
documentclass{article}
usepackage{geometry}
usepackage{amsmath,bm}
usepackage{tabularx,array}
usepackage{arydshln}

geometry{
  a4paper,
  total={170 mm,257 mm},
  left=20 mm,
  top=20 mm,
}

begin{document}

noindenttextbf{Solution:}
[
begin{tabularx}{textwidth}{@{} c | X @{}}
$begin{array}{cccccc}
         &   & 1 & 0 & 1 & 0 
  times &   &   & 1 & 0 & 1 
  hline
         & underline{1} & 1 & 0 & 1 & 0 
         & 0 & 0 & 0 & 0 &   
       1 & 0 & 1 & 0 &   &   
  hline
       1 & 1 & 0 & 0 & 1 & 0 
end{array}$ &
begin{tabular}{@{}p{linewidth}@{}}
As the product of binary multiplication would always be less than~$2$,
it won't generate any carry.
[2ex]
hdashline
[begin{array}{ccccccccc}
  & & textbf{Product/Sum} & & textbf{Base} & & textbf{Carry} & & textbf{Result} 
  1 + 0 + 1 & = & 2 > 1 & = & 2 & times & 1 & + & 0 [0.2 cm]   
end{array}]
end{tabular}
end{tabularx}
]

end{document}

Bernard · Answer

I propose this variant code, also based on tabularx, but using a matrix environment and Longstack for the part under the dashed line:
documentclass{article}
usepackage{geometry}
usepackage{amsmath,bm}
usepackage{tabularx}
usepackage{arydshln, booktabs,}
usepackage[usestackEOL]{stackengine}

geometry{a4paper, total={170 mm,257 mm}, left=20 mm, top=20 mm}

begin{document}

noindenttextbf{Solution:}
[
begin{tabularx}{textwidth}{@{} c | X @{}}
$begin{matrix}
         & & 1 & 0 & 1 & 0 
  times & & & 1 & 0 & 1 
  midrule
         & ^{underline{1}} & 1 & 0 & 1 & 0 
         & 0 & 0 & 0 & 0 & 
       1 & 0 & 1 & 0 & & 
  midrule
       1 & 1 & 0 & 0 & 1 & 0 
end{matrix}$enspace &
begin{tabular}{@{}p{linewidth}@{}}
As the product of binary multiplication would always be less than~$2$,
it won't generate any carry.
[2ex]
hdashline
stackMath
[ 1 + 0 + 1 = Longstack{textbf{Product/Sum}  2 > 1} = Longstack{ textbf{Base} 2} times Longstack{textbf{Carry} 1}
  + Longstack{textbf{Result}} ]
end{tabular}
end{tabularx}
]

end{document}

Issue with the alignment of the array

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