Re: Hexadecimal numbers

Tom Lisa Sun, 04 Mar 2001 16:27:13 -0800
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<font face="Times New Roman,Times"><font size=-1>Don't have a good site,
but perhaps this will help.&nbsp; BTW, this assumes</font></font>
<br><font face="Times New Roman,Times"><font size=-1>(and we all know how
dangerous that is) that you are fairly comfortable</font></font>
<br><font face="Times New Roman,Times"><font size=-1>with binary math.&nbsp;
If you aren't, I suggest you visit www.learntosubnet.com</font></font>
<br><font face="Times New Roman,Times"><font size=-1>and review their section
on binary math.</font></font><font face="Times New Roman,Times"><font 
size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>Converting from Hex
is quite simple if you use Binary as your conversion</font></font>
<br><font face="Times New Roman,Times"><font size=-1>medium or what I call
the Nibble Method.&nbsp; Since Hex is Base16 and Binary</font></font>
<br><font face="Times New Roman,Times"><font size=-1>is Base2, you can
think of Hex as shorthand for Binary.&nbsp; In Binary each</font></font>
<br><font face="Times New Roman,Times"><font size=-1>column position has
a range of two values ( 0 or 1 ).&nbsp; In Hex each column</font></font>
<br><font face="Times New Roman,Times"><font size=-1>position has a range
of sixteen values (0-9 &amp; A-F, where A=10, B=11,</font></font>
<br><font face="Times New Roman,Times"><font size=-1>C=12, D=12, E=14,
F=15).&nbsp; And finally, in Decimal each column position</font></font>
<br><font face="Times New Roman,Times"><font size=-1>has a range of ten
values (0 - 9).</font></font><font face="Times New Roman,Times"><font 
size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>From this we can see
that it takes four bit positions in binary to represent</font></font>
<br><font face="Times New Roman,Times"><font size=-1>all the possible values
of one hex position.&nbsp; For example, with one binary</font></font>
<br><font face="Times New Roman,Times"><font size=-1>nibble (four 
bits):</font></font><font face="Times New Roman,Times"><font size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>binary&nbsp;&nbsp;&nbsp;
hex&nbsp;&nbsp;&nbsp; binary&nbsp;&nbsp;&nbsp; hex&nbsp;&nbsp;&nbsp; 
binary&nbsp;&nbsp;&nbsp;
hex&nbsp;&nbsp;&nbsp; binary&nbsp;&nbsp;&nbsp; hex</font></font>
<br><font face="Times New Roman,Times"><font size=-1>&nbsp;0000&nbsp; =&nbsp;
0&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0100&nbsp; =&nbsp; 
4&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1000&nbsp; =&nbsp; 8&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1100&nbsp; =&nbsp;
C</font></font>
<br><font face="Times New Roman,Times"><font size=-1>&nbsp;0001&nbsp; =&nbsp;
1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0101&nbsp; =&nbsp; 
5&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1001&nbsp; =&nbsp; 9&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1101&nbsp; =&nbsp;
D</font></font>
<br><font face="Times New Roman,Times"><font size=-1>&nbsp;0010&nbsp; =&nbsp;
2&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0110&nbsp; =&nbsp; 
6&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1010&nbsp; =&nbsp; A&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1110&nbsp; =&nbsp;
E</font></font>
<br><font face="Times New Roman,Times"><font size=-1>&nbsp;0011&nbsp; =&nbsp;
3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0111&nbsp; =&nbsp; 
7&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1011&nbsp; =&nbsp; B&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1111&nbsp; =&nbsp;
F</font></font><font face="Times New Roman,Times"><font size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>Thus any two character
HEX number (as Hex is normally displayed) can be</font></font>
<br><font face="Times New Roman,Times"><font size=-1>converted to binary
simply by converting each character separately.</font></font><font face="Times New 
Roman,Times"><font size=-1></font></font>
<p><font face="Times New Roman,Times"><font 
size=-1>HEX:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
A&nbsp;&nbsp; 
D&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
E&nbsp;&nbsp;&nbsp; 7</font></font>
<br><font face="Times New Roman,Times"><font size=-1>thus</font></font>
<br><font face="Times New Roman,Times"><font size=-1>BINARY:&nbsp; 1010&nbsp;
1101&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1110&nbsp; 0111</font></font>
<br><font face="Times New Roman,Times"><font size=-1>thus</font></font>
<br><font face="Times New Roman,Times"><font size=-1>DECIMAL:&nbsp; 128+32+8+4+1
= 173&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 128+64+32+4+2+1 = 231</font></font>
<br><font face="Times New Roman,Times"><font size=-1>PROOF:&nbsp; 16^0=1,
D * 1 = 13*1 = 13</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16^1=16, A * 16 = 10 * 16 = 160</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
160 + 13 = 173</font></font><font face="Times New Roman,Times"><font 
size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>Larger Hex numbers
are also easily converted</font></font><font face="Times New Roman,Times"><font 
size=-1></font></font>
<p><font face="Times New Roman,Times"><font 
size=-1>HEX:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
6&nbsp;&nbsp; B&nbsp;&nbsp; F</font></font>
<br><font face="Times New Roman,Times"><font size=-1>thus</font></font>
<br><font face="Times New Roman,Times"><font size=-1>BINARY:&nbsp;&nbsp;&nbsp;
0110&nbsp; 1011&nbsp; 1111</font></font>
<br><font face="Times New Roman,Times"><font size=-1>thus</font></font>
<br><font face="Times New Roman,Times"><font size=-1>DECIMAL:&nbsp; 
1024+512+128+32+16+8+4+2+1
= 1727</font></font>
<br><font face="Times New Roman,Times"><font size=-1>PROOF:&nbsp;&nbsp;
16^0 = 1, F * 1 = 15 * 1 = 15</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16^1 = 16, B * 16 = 11 * 16 = 176</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16^2 = 256, 6 * 256 = 1536</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1536 + 176 + 15 = 1727</font></font><font face="Times New Roman,Times"><font 
size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>Going from Decimal
to Hex is just a reverse of the above process.</font></font>
<br><font face="Times New Roman,Times"><font size=-1>Convert the Decimal
number to Binary, divide the binary bits (working</font></font>
<br><font face="Times New Roman,Times"><font size=-1>right to left) into
Nibbles and then convert each Nibble to Hex.</font></font><font face="Times New 
Roman,Times"><font size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>When converting Decimal
to Binary I prefer the division by two method.</font></font>
<br><font face="Times New Roman,Times"><font size=-1>You divide the Decimal
number by two and the remainder becomes the</font></font>
<br><font face="Times New Roman,Times"><font size=-1>first binary bit,
working from right to left.</font></font><font face="Times New Roman,Times"><font 
size=-1></font></font>
<p><font face="Times New Roman,Times"><font size=-1>DECIMAL:&nbsp;&nbsp;
792</font></font>
<br><font face="Times New Roman,Times"><font size=-1>CONVERSION:&nbsp;
792/2 = 396 Remainder 0,&nbsp; BINARY =&nbsp; 0</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
396/2 = 198 Remainder 0,&nbsp; BINARY = 00</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
198/2 =&nbsp;&nbsp; 99 Remainder 0,&nbsp; BINARY = 000</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
99/2 =&nbsp;&nbsp; 49 Remainder 1,&nbsp; BINARY = 1000</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
49/2 =&nbsp;&nbsp; 24 Remainder 1,&nbsp; BINARY = 1 1000</font></font>
<br><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
24/2 =&nbsp;&nbsp; 12 <font face="Times New Roman,Times">Remainder 0,&nbsp;
BINARY = 01 1000</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
12/2 =&nbsp;&nbsp;&nbsp;&nbsp; 6 Remainder 0,&nbsp; BINARY = 001 1000</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
6/2 =&nbsp;&nbsp;&nbsp;&nbsp; 3 Remainder 0,&nbsp; BINARY = 0001 1000</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
3/2 =&nbsp;&nbsp;&nbsp;&nbsp; 1 Remainder 0,&nbsp; BINARY = 1 0001 1000</font></font>
<br><font face="Times New Roman,Times"><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1/2 =&nbsp;&nbsp;&nbsp;&nbsp; 0 Remainder 1,&nbsp; BINARY = 0011 0001 
1000</font></font>
<br><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
^^ Padded to make a nibble</font>
<br><font size=-1>BINARY:&nbsp;&nbsp; 0011&nbsp; 0001&nbsp; 1000</font>
<br><font size=-1>HEX:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
3&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
1&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
8</font>
<br><font size=-1>PROOF:&nbsp; 16^0 = 1, 1 * 8 = 8</font>
<br><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16^1 = 16, 16 * 1 = 16</font>
<br><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16^2 = 256, 256 * 3 = 768</font>
<br><font 
size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
768+16+8 = 792</font><font size=-1></font>
<p><font size=-1>Another method was provided by Priscilla in a response
to a similar question by</font>
<br><font size=-1>someone else.&nbsp; Whichever you use, just remember
that practice is the key to</font>
<br><font size=-1>understanding.</font><font size=-1></font>
<p><font size=-1>HTH,</font><font size=-1></font>
<p><font size=-1>Tom Lisa, Instructor, CCNA, CCAI</font>
<br><font size=-1>Community College of Southern Nevada</font>
<br><font size=-1>Cisco Regional Networking Academy</font>
<br><font size=-1></font>&nbsp;
<br><font size=-1></font>&nbsp;<font size=-1></font>
<p>[EMAIL PROTECTED] wrote:
<blockquote TYPE=CITE>Does anyone know a good Web site to learn about the
Structure of Hex Numbers
<br>and how to convert, from Hex to&nbsp; Binary, to Dec and back and forth
between
<br>the systems and IPX Addresses also.
<p>TIA,
<p>Jess
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Re: Hexadecimal numbers

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