mjhjmtu

This is the result I want to have (I want to obtain the result that most resembles this mathematical expression):

What I have tried is this:

[
beginaligned
 01: 1011 : 0110\
 11: 0001 : 1101\
 hline
 11: 1011 : 1111\
 01: 0001 : 0100\
 10: 1010 : 1011
endaligned
]

Result:

I don't know how to insert the text "bitwise OR", "bitwise AND" and also to reduce the spacing between the numbers.

PD: The font color doesn't matter.

You can usa a tabular, with booktabs and its prettier rules.

I chose to typeset four columns, so you can decide upon the spacing as you please; I find thinspace better. You can use hspace<length> as you please instead. Also $:$ would do, if you prefer that space.

documentclassarticle
usepackagebooktabs,array

newcolumntypeR>$r<$ % right aligned math

begindocument

[
begintabular
 @
 R@thinspace
 R@thinspace
 R
 l
 @

01 & 1011 & 0110\
11 & 0001 & 1101\
cmidrule[lightrulewidth](r)1-3
11 & 1011 & 1111 & bitwise OR \
01 & 0001 & 0100 & bitwise AND \
10 & 1010 & 1011 & bitwise XOR
endtabular
]

enddocument

Is this what you want?

begintabular@ccc@c l
 01& 1011 & 0110\
 11& 0001 & 1101\
 cline1-3
 11& 1011 & 1111 && bitwise textitOR\
 01& 0001 & 0100 && bitwise textitAND \
 10& 1010 & 1011 && bitwise textitXOR
endtabular

Of course, someone needs to show how to do this with a matrix construct in TikZ.

documentclass[border=6pt]standalone

usepackagetikz
usetikzlibrarycalc
usetikzlibrarymatrix

begindocument

begintikzpicture

 matrix (BINARY)
 [matrix of nodes,
 row sep=4pt,
 nodes=font=sffamily,]
 
 01 & 1011 & 0110 \
 11 & 0001 & 1101 \
 %% -----------------
 11 & 1011 & 1111 \%% bitwise OR 
 01 & 0001 & 0100 \%% bitwise AND 
 10 & 1010 & 1011 \%% bitwise XOR 
 ;

 draw ($(BINARY-2-1.south west)!0.5!(BINARY-3-1.north west)$) -- 
 ($(BINARY-2-3.south east)!0.5!(BINARY-3-3.north east)$);

 node[anchor=west,blue] at (BINARY-3-3.east) bitwise OR;
 node[anchor=west,blue] at (BINARY-4-3.east) bitwise AND;
 node[anchor=west,blue] at (BINARY-5-3.east) bitwise XOR;

endtikzpicture

enddocument

For the comments on last three rows you could, alternatively, use a foreach loop as follows:

foreach myn/myop in 3/OR,4/AND,5/XOR
 
 node[anchor=west,blue] at (BINARY-myn-3.east) bitwise myop; 
 

You alse can use the alignedat environment to have full control on the spacing:

documentclassarticle
usepackagemathtools
usepackage[svgnames, table]xcolor
usepackagebooktabs, hhline

begindocument

[ aboverulesep = -2.5exbelowrulesep = -1exarrayrulecolorSkyBlue
beginalignedat4
 & 01 & : & 1011 & : & 0110\
 & 11 & : & 0001 & : & 1101\
 cmidrule[0.15ex]1-6
 & 11 & : & 1011 & : & 1111 &qquad &textcolorSkyBluebitwise emphOR \
 & 01 & : & 0001 & : & 0100 & & textcolorSkyBluebitwise emphAND\
 & 10 & : & 1010 & : & 1011 & & textcolorSkyBluebitwise emphXOR
endalignedat
]

enddocument