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<DIV dir=ltr align=left><FONT color=#0000ff face=Arial><SPAN
class=673443413-18082021>As promised, I checked how I originally defined this
for decimal numbers; links to the full document are at: <A
href="http://speleotrove.com/decimal/#arithmetic">http://speleotrove.com/decimal/#arithmetic</A></SPAN></FONT></DIV>
<DIV dir=ltr align=left><FONT color=#0000ff face=Arial><SPAN
class=673443413-18082021></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT color=#0000ff face=Arial><SPAN
class=673443413-18082021>The most pertinent section is at: <A
href="http://speleotrove.com/decimal/damodel.html">http://speleotrove.com/decimal/damodel.html</A> which
states:</SPAN></FONT></DIV>
<BLOCKQUOTE style="MARGIN-RIGHT: 0px" dir=ltr>
<DIV><FONT color=#0000ff size=2 face=Arial><SPAN
class=673443413-18082021><SPAN
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial'>"In
any context where exponents are bounded most finite numbers
are<SPAN> </SPAN></SPAN><I
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); ORPHANS: 2; WIDOWS: 2; LETTER-SPACING: normal; TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; text-decoration-line: none'>normal</I><SPAN
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial'>.
Non-zero finite numbers whose adjusted exponents are greater than or equal to
E</SPAN><SUB
style='FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; LETTER-SPACING: normal; TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; text-decoration-line: none'><FONT
size=3>min</FONT></SUB><SPAN
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial'><SPAN> </SPAN>are
called<SPAN> </SPAN></SPAN><I
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); ORPHANS: 2; WIDOWS: 2; LETTER-SPACING: normal; TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; text-decoration-line: none'>normal</I><SPAN
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial'><SPAN> </SPAN>numbers;
those non-zero numbers whose adjusted exponents are less than E</SPAN><SUB
style='FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; LETTER-SPACING: normal; TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; text-decoration-line: none'><FONT
size=3>min</FONT></SUB><SPAN
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial'><SPAN> </SPAN>are
called<SPAN> </SPAN></SPAN><I
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); ORPHANS: 2; WIDOWS: 2; LETTER-SPACING: normal; TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; text-decoration-line: none'>subnormal</I><SPAN
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial'><SPAN> </SPAN>numbers."</SPAN></SPAN></FONT></DIV><FONT
color=#0000ff size=2 face=Arial><SPAN class=673443413-18082021><SPAN
style='FONT-SIZE: medium; FONT-FAMILY: "Times New Roman"; WHITE-SPACE: normal; WORD-SPACING: 0px; TEXT-TRANSFORM: none; FLOAT: none; FONT-WEIGHT: 400; COLOR: rgb(0,0,0); FONT-STYLE: normal; ORPHANS: 2; WIDOWS: 2; DISPLAY: inline !important; LETTER-SPACING: normal; BACKGROUND-COLOR: rgb(255,255,255); TEXT-INDENT: 0px; font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial'>
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<TD style="TEXT-DECORATION: none !important"><FONT
style="TEXT-DECORATION: none !important" size=2><A
style="TEXT-DECORATION: none !important"
href="http://speleotrove.com/decimal/damodel.html#backref.8">[8]</A></FONT></TD>
<TD style="TEXT-DECORATION: none !important"><FONT
style="TEXT-DECORATION: none !important" size=2>That is, numbers whose
absolute value is non-zero and is closer to zero than ten to the power
of E<SUB
style="TEXT-DECORATION: none !important">min</SUB>.</FONT></TD></TR></TBODY></TABLE></DIV><SPAN
class=673443413-18082021></BLOCKQUOTE>
<DIV dir=ltr><FONT face=Arial><FONT color=#0000ff><FONT size=3>'Adjusted
exponent' is defined earlier in that section<SPAN class=673443413-18082021>, and
is, in effect, a normalized exponent but described independently of encodings
etc.</SPAN></FONT></FONT></FONT></DIV>
<DIV dir=ltr><FONT color=#0000ff size=3 face=Arial></FONT> </DIV>
<DIV dir=ltr><SPAN class=673443413-18082021><FONT color=#0000ff size=3
face=Arial>This does avoid the use of the term 'normalized', which perhaps
avoids the entanglement we discussed yesterday.</FONT></SPAN></DIV>
<DIV dir=ltr><FONT color=#0000ff size=3 face=Arial></FONT> </DIV>
<DIV dir=ltr></SPAN><SPAN class=673443413-18082021><FONT color=#0000ff size=3
face=Arial>Mike</FONT></SPAN></DIV>
<DIV style="MARGIN-RIGHT: 0px" dir=ltr></SPAN></SPAN></FONT> </DIV>
<DIV dir=ltr align=left><FONT color=#0000ff size=2 face=Arial><SPAN
class=673443413-18082021></SPAN></FONT> </DIV></BODY></HTML>