CompTIA

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=2 height=90 BGCOLOR="#006699" TEXT="#080000" background="005785a3.jpg"> <div> <FONT SIZE="5" COLOR="#FFFFFF" FACE="Arial" ><B>NBeqo's Website</B></FONT><B>    </B><B> |     </B><A HREF="index.htm" TARGET="_top" TITLE="NBeqos Website"><U><B>home</B></U></A></div> <div> <B>CompTIA</B>   |   <A HREF="id20.htm" TARGET="_top" TITLE="Microsoft"><U>Microsoft</U></A>   |   <A HREF="id10.htm" TARGET="_top" TITLE="CISCO"><U>CISCO</U></A>   |   <A HREF="id50.htm" TARGET="_top" TITLE="IBM"><U>IBM</U></A>   |   <A HREF="id46.htm" TARGET="_top" TITLE="Telecom"><U>Telecom</U></A>   |   <A HREF="id32.htm" TARGET="_top" TITLE="Desktop Publishing"><U>Desktop Publishing</U></A>   |   <A HREF="id11.htm" TARGET="_top" TITLE="Maintenance"><U>Maintenance</U></A></div> <div> </div> </td> </tr><tr> <td valign="top" width=13.875% BGCOLOR="#FFCC66" TEXT="#080000"> <bR> <div> <A HREF="id15.htm" TARGET="_top" TITLE="Linux"><U><B>Linux+</B></U></A></div> <div> <A HREF="id18.htm" TARGET="_top" TITLE="Network"><U><B>Network+</B></U></A></div> <div> <A HREF="id26.htm" TARGET="_top" TITLE="Security"><U><B>Security+</B></U></A></div> <bR> </td> <td valign="top" height=390 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <I>CompTIA</I></div> <bR> <div> <B>Bits and Bytes</B></div> <bR> <div> <B>Binary</B> system uses Base 2, which means 2 placeholders, 0 and 1. Computers count in bits (0 = off and 1=on): 10001110101011110000111010001000..... etc. However, it is not easy for humans to remember all these 1s and 0s, so we divide the bits in octets (8) and count from the right to the left: Remember that 0 is a real number when dealing with binary, i.e., from 0 to 255 there are 256 bits. </div> <bR> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="415" BORDERCOLORLIGHT="#FFFBF0" BORDERCOLORDARK="#EEEEEE" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 16 ><NOBR><div> 1 0 0 0 1 1 1 0 .</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div>  1 0 1 0 1 1 1 1 .</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 0 0 0 0 1 1 1 0 . </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 1 0 0 0 1 0 0 0.</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 ><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> </tR> </TABLE></div> <div> Table 1</div> <bR> <div> <B>Possible patterns of 0s and 1s</B></div> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="281" BORDERCOLORLIGHT="#FFFBF0" BORDERCOLORDARK="#EEEEEE" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> <I>3 bits</I></div> </tD> <tD VALIGN=TOP WIDTH="88"><div> <I>2 bits</I></div> </tD> <tD VALIGN=TOP WIDTH="85"><div> <I>1bit</I></div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 0 0 0</div> </tD> <tD VALIGN=TOP WIDTH="88"><div> 0 0</div> </tD> <tD VALIGN=TOP WIDTH="85"><div> 0</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 0 0 1</div> </tD> <tD VALIGN=TOP WIDTH="88"><div> 0 1</div> </tD> <tD VALIGN=TOP WIDTH="85"><div> 1</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 0 1 0</div> </tD> <tD VALIGN=TOP WIDTH="88"><div> 1 0</div> </tD> <tD VALIGN=TOP WIDTH="85"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="85" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 0 1 1</div> </tD> <tD VALIGN=TOP WIDTH="88"><div> 1 1</div> </tD> <tD VALIGN=TOP WIDTH="85"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="85" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 1 0 0</div> </tD> <tD VALIGN=TOP WIDTH="88"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="88" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="85"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="85" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 1 0 1</div> </tD> <tD VALIGN=TOP WIDTH="88"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="88" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="85"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="85" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 1 1 0</div> </tD> <tD VALIGN=TOP WIDTH="88"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="88" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="85"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="85" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="90"><div> 1 1 1</div> </tD> <tD VALIGN=TOP WIDTH="88"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="88" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="85"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="85" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 ><NOBR><div> Total: 8 (2^3)</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> Total: 4 (2^2)</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> Total: 2 (2^1)</div> </NOBR></tD> </tR> </TABLE></div> <div> Table 2</div> <bR> <div> <I>Question:</I> What's the total patterns of 0s and 1s with 4bits; 5bits; 6bits; 7bits; 8 bits; n bits?</div> <div> <I>Answer:</I> 2^4=16; 2^5=32; 2^6=64; 2^7=128; 2^8=256; 2^n.</div> <bR> <div> <B>Converting binary into decimal numbers:</B></div> <div> To make our life easy, in each octet we replace the bits that are turned on (bit 1) with the value of the total number of posible patterns. <I>Adding</I> the position value of each bit that is turned on (1)  gives us a decimal number that represents the entire octet :</div> <bR> <div> <TABLE BORDER="1" CELLPADDING="0" CELLSPACING="0" WIDTH="298" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#EEEEEE" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 20 WIDTH="91"><div> Bits</div> </tD> <tD VALIGN=TOP WIDTH="30"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> </tR> <tR> <tD VALIGN=TOP ROWSPAN=2 HEIGHT= 16 ><NOBR><bR> <div> Position Power</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="30"><div> 7</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 6</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 5</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> </tR> <tR> <tD VALIGN=TOP WIDTH="30"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="25"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="20"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 2</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 32 ><NOBR><bR> <div> Position Value</div> </NOBR></tD> <tD VALIGN=TOP WIDTH="30"><bR> <div> 128</div> </tD> <tD VALIGN=TOP WIDTH="25"><bR> <div> 64</div> </tD> <tD VALIGN=TOP WIDTH="25"><bR> <div> 32</div> </tD> <tD VALIGN=TOP WIDTH="25"><bR> <div> 16</div> </tD> <tD VALIGN=TOP WIDTH="20"><bR> <div> 8</div> </tD> <tD VALIGN=TOP WIDTH="20"><bR> <div> 4</div> </tD> <tD VALIGN=TOP WIDTH="20"><bR> <div> 2</div> </tD> <tD VALIGN=TOP WIDTH="22"><bR> <div> 1</div> </tD> </tR> </TABLE></div> <div> Table 3</div> <bR> <div> Therefore, the octet with all 1s is represented by the decimal 255 (128+64+32+16+8+4+2+1)</div> <bR> <div> <I>Example:</I> Let's convert binary to decimal for Table1:</div> <div> In the first octet of Table 1 we have: 2^7 = 128; 2^3 = 8; 2^2 = 4; 2^1 = 2. We add these values up: 128+8+4+2=142 and the total will represent the entire octet. Do the same for the other octets:</div> <bR> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="415" BORDERCOLORLIGHT="#FFFBF0" BORDERCOLORDARK="#EEEEEE" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 16 ><NOBR><div> 1 0 0 0 1 1 1 0 .</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div>  1 0 1 0 1 1 1 1 .</div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 0 0 0 0 1 1 1 0 . </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 1 0 0 0 1 0 0 0.</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 ><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> 7 6 5 4 3 2 1 0 </div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="98"><div> 142.</div> </tD> <tD VALIGN=TOP WIDTH="101"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="101" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="98"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="98" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="95"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="95" HSPACE="0" VSPACE="0"></tD> </tR> </TABLE></div> <bR> <bR> <div> <I>Practice the following table: </I></div> <bR> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="564" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#EEEEEE" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 128</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 64</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 32</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 16</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 8</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="48" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="28"><div> 128</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 64</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 32</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 16</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 8</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="48" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=8 HEIGHT= 16 WIDTH="209"><div> Computers</div> </tD> <tD VALIGN=TOP><NOBR><div> Humans</div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=8 WIDTH="206"><div> Computers</div> </tD> <tD VALIGN=TOP><NOBR><div> Humans</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 128</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 127</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 192</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 63</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 224</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 31</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 240</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 15</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 248</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 7</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 252</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 3</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 254</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 1</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="28"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="24"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 255</div> </tD> <tD VALIGN=TOP WIDTH="28"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="23"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> </tR> </TABLE></div> <div> Table 4</div> <bR> <div> <I>Practice without using the table: </I></div> <div> What's the decimal number for 01111111; 11111110; 00111111; 11111100; 00011111; 11111000; 00001111; 11110000; 00000111; 11100000; 00000011; 11000000?</div> <bR> <div> <I>Exercise</I>: Convert from Decimal system into the Binary system and vice-versa:</div> <div>  ? = 96; ? = 48; ? = 24; ? = 80; ? = 100;  01010101= ?; 10101010 = ?; 11100010 = ?;  10100010 = ?</div> <bR> <div> <B>AND -ing bits</B>: 1+1=1, everything else is 0:   </div> <div> 10101010 </div> <div> <U>11100010 </U></div> <div> 10100010 </div> <bR> <div> To AND two decimal numbers, we convert them to binary, AND the binaries and convert the result back to decimal.</div> <bR> <div> Example: AND 248 with 76      </div> <div> 11111000    (248)</div> <div> <U>01001100</U>    ( 76 )</div> <div> 01001000    ( 72 )</div> <div> Answer: 248 AND 76 = 72</div> <bR> <div> <I>Exercise</I>: AND 192 with 63; 224 with 31; 240 with 15; 248 with 7; 252 with 3.  </div> <div>    </div> <bR> <div> <B>Hexadecimal</B> (Hexa = 6, Decimal = 10) system uses Base 16 (16 place holders: 0 to 9 and A to F)</div> <bR> <div> <TABLE BORDER="2" CELLPADDING="1" CELLSPACING="1" WIDTH="327" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#EEEEEE" FRAME="BOX" RULES="ALL" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 8</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="48" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP WIDTH="22"><div> 8</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="16" ALIGN="bottom" WIDTH="48" HSPACE="0" VSPACE="0"></tD> </tR> <tR> <tD VALIGN=TOP COLSPAN=4 HEIGHT= 16 WIDTH="97"><div> Computer</div> </tD> <tD VALIGN=TOP><NOBR><div> Human</div> </NOBR></tD> <tD VALIGN=TOP COLSPAN=4 WIDTH="97"><div> Computer</div> </tD> <tD VALIGN=TOP><NOBR><div> Human</div> </NOBR></tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 8</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 9</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 2</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> A</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 3</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> B</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 4</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> C</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 5</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> D</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 6</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> E</div> </tD> </tR> <tR> <tD VALIGN=TOP HEIGHT= 16 WIDTH="22"><div> 0</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> 7</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="22"><div> 1</div> </tD> <tD VALIGN=TOP WIDTH="48"><div> F</div> </tD> </tR> </TABLE></div> <bR> <bR> <div> Note: Convert from Hexadecimal to binary and then to Decimal.</div> <bR> <bR> <div> <B>Features of checksum</B></div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">It's more powerful than parity</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">If two bits in exactly the same place in two separate data units are damaged, the error will go undetected</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">If some data is damaged, the whole block is descarded</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Burst errors may cancel each other out, rendering the checksum useless</div> <bR> <bR> <div> <B>The CRC process</B></div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Each data unit received in a transmission is <I>examined</I>.</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">A sequence of 0s is <I>appended</I> to the data unit.</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">A  predetermined binary divisor is used to divide the new data unit and <I>produce a CRC</I></div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">The resulting CRC is <I>appended</I> to the original data unit and the data is transmitted</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">The CRC checker of the <I>receiver</I> treats the CRC and data as one data unit and <I>divides</I> it by using the divisor</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">If the result of the division is a nonzero remainder, a retransmission is requested. If the remainder is zero, the data unit passes.</div> <bR> <div> <B>Synchronous transmission</B></div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Iddle data sequences are sent to create transmission gaps</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Transmitted data can be sent with a timing signal</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">DCE for synchronous modems is expensive</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">The user can send more data in less time</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Data is encoded by using framing protocols</div> <bR> <bR> <div> <B>Asynchronous transmission</B></div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Gaps in the data streams make the transmission slow</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">It's a form of a serial transmission</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Each byte sent has three overheads</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">It uses start and stop bits to coordinate transmission</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">It's not very cost effective</div> <bR> <bR> <div> <B>Features of a framing protocol</B></div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">It's a set of rules that the DCE follows to organize data into frames</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">It encodes control signals into messages</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">There are two types, bit-oriented and byte-oriented</div> <div> <IMG BORDER="0" SRC="Symb075c00b700c800000000.png" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">A bit-oriented framing protocol is more efficient than a byte-oriented framing protocol</div> <bR> <bR> <bR> </td> </tr></table></body>