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<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT><A NAME='7'><FONT COLOR=red>#&nbsp;MATH introduce a simple form of binary notation</FONT></A></TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>#&nbsp;After this lesson, in the higher-level version of the message,</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>#&nbsp;will expand decimal to stand for the binary notation given.</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>#&nbsp;It wouldn't be hard to accompany this lesson with a more</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>#&nbsp;formal definition once functions are introduced (below)</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>#&nbsp;so maybe the transition to binary should be delayed?</TT><BR>
<TT>[<A HREF='sound.cgi?s=21032130102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:)</font> 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210301102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.)</font> 0110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210030111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..)</font> 011110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321000301111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:...)</font> 0111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321000030111111111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:....)</font> 011111111111111110);</TT><BR>
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<TT>[<A HREF='sound.cgi?s=2103203002233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(.)</font> 00);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032130102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:)</font> 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210301102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.)</font> 0110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032113011102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::)</font> 01110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210030111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..)</font> 011110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032101301111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:)</font> 0111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321103011111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::.)</font> 01111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103211130111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:::)</font> 011111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321000301111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:...)</font> 0111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210013011111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..:)</font> 01111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032101030111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:.)</font> 011111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321011301111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.::)</font> 0111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103211003011111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::..)</font> 01111111111110);</TT><BR>
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<TT>[<A HREF='sound.cgi?s=21032110130111111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::.:)</font> 011111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321110301111111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:::.)</font> 0111111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103211113011111111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::::)</font> 01111111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103203002233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(.)</font> 00);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103211130111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:::)</font> 011111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032110130111111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::.:)</font> 011111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032101301111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:)</font> 0111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210013011111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..:)</font> 01111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103203002233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(.)</font> 00);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032113011102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::)</font> 01110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103211113011111111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::::)</font> 01111111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103211003011111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::..)</font> 01111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032101301111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:)</font> 0111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032101301111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:)</font> 0111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210013011111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..:)</font> 01111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210301102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.)</font> 0110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032130102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:)</font> 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103211113011111111111111102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::::)</font> 01111111111111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210301102233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.)</font> 0110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210301111100232101030111100102233'>hear</A>] </TT><TT>(= 0111110 / + 011110 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321013023210103210032132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:)</font> / + <font style='background-color: #ffcdff'>(:..)</font> <font style='background-color: #ffffcd'>(:)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103011111110023210103011111100102233'>hear</A>] </TT><TT>(= 011111110 / + 01111110 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321113023210103211032132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:::)</font> / + <font style='background-color: #ffcdff'>(::.)</font> <font style='background-color: #ffffcd'>(:)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210301111100232101030111100102233'>hear</A>] </TT><TT>(= 0111110 / + 011110 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321013023210103210032132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:)</font> / + <font style='background-color: #ffcdff'>(:..)</font> <font style='background-color: #ffffcd'>(:)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103011110023210103000111102233'>hear</A>] </TT><TT>(= 011110 / + 00 011110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321003023210103203210032233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..)</font> / + <font style='background-color: #ffcdff'>(.)</font> <font style='background-color: #ffffcd'>(:..)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21030111111111002321010301111111001102233'>hear</A>] </TT><TT>(= 01111111110 / + 011111110 0110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032100130232101032111321032233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..:)</font> /</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>&nbsp;&nbsp;+ <font style='background-color: #ffcdff'>(:::)</font> <font style='background-color: #ffffcd'>(:.)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210301111111111100232101030111111100111102233'>hear</A>] </TT><TT>(= 0111111111110 / + 011111110 011110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321011302321010321113210032233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.::)</font> /</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>&nbsp;&nbsp;+ <font style='background-color: #ffcdff'>(:::)</font> <font style='background-color: #ffffcd'>(:..)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103011111111110023210103011100111111102233'>hear</A>] </TT><TT>(= 011111111110 / + 01110 011111110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21032101030232101032113211132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:.:.)</font> /</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>&nbsp;&nbsp;+ <font style='background-color: #ffcdff'>(::)</font> <font style='background-color: #ffffcd'>(:::)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21030111111002321010301111100102233'>hear</A>] </TT><TT>(= 01111110 / + 0111110 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321103023210103210132132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::.)</font> / + <font style='background-color: #ffcdff'>(:.:)</font> <font style='background-color: #ffffcd'>(:)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21030111100232100130111100102233'>hear</A>] </TT><TT>(= 011110 / * 011110 010);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321003023210013210032132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..)</font> / * <font style='background-color: #ffcdff'>(:..)</font> <font style='background-color: #ffffcd'>(:)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21030111100232100130100111102233'>hear</A>] </TT><TT>(= 011110 / * 010 011110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321003023210013213210032233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..)</font> / * <font style='background-color: #ffcdff'>(:)</font> <font style='background-color: #ffffcd'>(:..)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21030111100232100130100111102233'>hear</A>] </TT><TT>(= 011110 / * 010 011110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321003023210013213210032233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..)</font> / * <font style='background-color: #ffcdff'>(:)</font> <font style='background-color: #ffffcd'>(:..)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103011111100232100130110011102233'>hear</A>] </TT><TT>(= 01111110 / * 0110 01110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321103023210013210321132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::.)</font> / * <font style='background-color: #ffcdff'>(:.)</font> <font style='background-color: #ffffcd'>(::)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103011111100232100130110011102233'>hear</A>] </TT><TT>(= 01111110 / * 0110 01110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321103023210013210321132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(::.)</font> / * <font style='background-color: #ffcdff'>(:.)</font> <font style='background-color: #ffffcd'>(::)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103011110023210013011001102233'>hear</A>] </TT><TT>(= 011110 / * 0110 0110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=210321003023210013210321032233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..)</font> / * <font style='background-color: #ffcdff'>(:.)</font> <font style='background-color: #ffffcd'>(:.)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21030111111111002321001301110011102233'>hear</A>] </TT><TT>(= 01111111110 / * 01110 01110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210013023210013211321132233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:..:)</font> /</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>&nbsp;&nbsp;* <font style='background-color: #ffcdff'>(::)</font> <font style='background-color: #ffffcd'>(::)</font>);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=21030111111111111111100232100130111100111102233'>hear</A>] </TT><TT>(= 011111111111111110 / * 011110 011110);</TT><BR>
<BR>
<TT>[<A HREF='sound.cgi?s=2103210000302321001321003210032233'>hear</A>] </TT><TT>(= <font style='background-color: #cdffff'>(:....)</font> /</TT><BR>
<TT>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TT><TT>&nbsp;&nbsp;* <font style='background-color: #ffcdff'>(:..)</font> <font style='background-color: #ffffcd'>(:..)</font>);</TT><BR>
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