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< p > Grouping V0:< / p >
< p > < span class = "katex-display" > < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mtext > 1001< / mtext > < mn > 2< / mn > < / msub > < mo > +< / mo > < msub > < mtext > 0110< / mtext > < mn > 2< / mn > < / msub > < mo > =< / mo > < msub > < mtext > 1111< / mtext > < mn > 2< / mn > < / msub > < / mrow > < annotation encoding = "application/x-tex" >
\text{1001}_{2} + \text{0110}_{2} = \text{1111}_{2}
< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.79444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > 1001< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < span class = "mbin" > +< / span > < span class = "mspace" style = "margin-right:0.2222222222222222em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.79444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > 0110< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.79444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > 1111< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< p > Grouping V1: < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mtext > 512< / mtext > < mn > 10< / mn > < / msub > < mo > =< / mo > < msubsup > < mn > 2< / mn > < mn > 10< / mn > < mn > 9< / mn > < / msubsup > < mo > =< / mo > < msub > < mtext > 111111111< / mtext > < mn > 2< / mn > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \text{512}_{10} = 2^{9}_{10} = \text{111111111}_{2}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.79444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > 512< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 10< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0622159999999998em;vertical-align:-0.24810799999999997em;" > < / span > < span class = "mord" > < span class = "mord" > 2< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8141079999999999em;" > < span style = "top:-2.4518920000000004em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 10< / span > < / span > < / span > < / span > < span style = "top:-3.063em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 9< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.24810799999999997em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.79444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord text" > < span class = "mord" > 111111111< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< p > Grouping V2: < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mn mathvariant = "italic" > 512< / mn > < mn > 10< / mn > < / msub > < mo > =< / mo > < msubsup > < mn > 2< / mn > < mn > 10< / mn > < mn > 9< / mn > < / msubsup > < mo > =< / mo > < msub > < mn mathvariant = "italic" > 111111111< / mn > < mn > 2< / mn > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \mathit{512}_{10} = 2^{9}_{10} = \mathit{111111111}_{2}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:0.79444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathit" > 512< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 10< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:1.0622159999999998em;vertical-align:-0.24810799999999997em;" > < / span > < span class = "mord" > < span class = "mord" > 2< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8141079999999999em;" > < span style = "top:-2.4518920000000004em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 10< / span > < / span > < / span > < / span > < span style = "top:-3.063em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 9< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.24810799999999997em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < / span > < span class = "base" > < span class = "strut" style = "height:0.79444em;vertical-align:-0.15em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord mathit" > 111111111< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mtight" > 2< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
< p > Grouping V3: < span class = "katex" > < span class = "katex-mathml" > < math xmlns = "http://www.w3.org/1998/Math/MathML" > < semantics > < mrow > < msub > < mn mathvariant = "italic" > 512< / mn > < mn mathvariant = "italic" > 10< / mn > < / msub > < mo > =< / mo > < msubsup > < mn mathvariant = "italic" > 2< / mn > < mn mathvariant = "italic" > 10< / mn > < mn mathvariant = "italic" > 9< / mn > < / msubsup > < mo > =< / mo > < msub > < mn mathvariant = "italic" > 111111111< / mn > < mn mathvariant = "italic" > 2< / mn > < / msub > < / mrow > < annotation encoding = "application/x-tex" > \it{512}_{10} = 2^{9}_{10} = \it{111111111}_{2}< / annotation > < / semantics > < / math > < / span > < span class = "katex-html" aria-hidden = "true" > < span class = "base" > < span class = "strut" style = "height:1.0622159999999998em;vertical-align:-0.24810799999999997em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord" > < span class = "mord mathit" > 512< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathit mtight" > 10< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mord" > < span class = "mord mathit" > 2< / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.8141079999999999em;" > < span style = "top:-2.4518920000000004em;margin-left:0em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathit mtight" > 10< / span > < / span > < / span > < / span > < span style = "top:-3.063em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathit mtight" > 9< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.24810799999999997em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mrel" > =< / span > < span class = "mspace" style = "margin-right:0.2777777777777778em;" > < / span > < span class = "mord" > < span class = "mord" > < span class = "mord" > < span class = "mord mathit" > 111111111< / span > < / span > < span class = "msupsub" > < span class = "vlist-t vlist-t2" > < span class = "vlist-r" > < span class = "vlist" style = "height:0.30110799999999993em;" > < span style = "top:-2.5500000000000003em;margin-right:0.05em;" > < span class = "pstrut" style = "height:2.7em;" > < / span > < span class = "sizing reset-size6 size3 mtight" > < span class = "mord mtight" > < span class = "mord mathit mtight" > 2< / span > < / span > < / span > < / span > < / span > < span class = "vlist-s" > < / span > < / span > < span class = "vlist-r" > < span class = "vlist" style = "height:0.15em;" > < span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / span > < / p >
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