tag:blogger.com,1999:blog-53170092501998808162024-09-24T08:57:10.733-07:00satpanhttp://www.blogger.com/profile/02844676451849547823noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5317009250199880816.post-70906421217393349522012-06-01T11:12:00.004-07:002012-06-17T10:00:02.555-07:00<div dir="ltr" style="text-align: left;" trbidi="on"> <br /> <br /> <b>FIRST convert a Gray-coded number to binary by follow this method :-</b><br /> The binary number and the Gray-coded number will have the same number of bits<br /> <br /> 1. The binary MSB (left-hand bit) and Gray code MSB will always be the same<br /> <br /> 2. To get the binary next-to-MSB (i.e. next digit to the right) add the binary MSB and the gray code next-to-MSB.<br /> <br /> 3. Record the sum, ignoring any carry.<br /> <br /> 4. Continue in this manner right through to the end.<br /> <br /> example:- <br /> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">Gray Code&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Conversion &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Binary Code</span></div> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">&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; G<span style="font-size: x-small;">msb+1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span style="font-size: large;">B<span style="font-size: x-small;">msb</span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">111&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;"><span style="background-color: white;"><span style="background-color: red;">1</span>&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; <span style="background-color: red;">1<span style="background-color: white;">&nbsp;</span><span style="background-color: white;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)</span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">1</span></span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">11&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp; &nbsp; + &nbsp;&nbsp; </span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">= 1</span><span style="background-color: lime; font-size: large;">0</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span style="background-color: white;">1</span></span><span style="background-color: lime; font-size: large;">0<span style="background-color: white;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2), (3)</span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">11</span></span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">1&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp; +&nbsp;&nbsp;&nbsp; </span><span style="background-color: lime; font-size: large;">0</span><span style="font-size: large;">=&nbsp;&nbsp; <span style="background-color: red;">1</span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">1</span><span style="background-color: white; font-size: large;">0</span><span style="background-color: red; font-size: large;">1<span style="background-color: white;">&nbsp;&nbsp;&nbsp;&nbsp; (4)</span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">111</span></span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp; +&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">= 1</span><span style="background-color: lime; font-size: large;">0</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">1</span><span style="background-color: white; font-size: large;">0</span><span style="background-color: white; font-size: large;">1</span><span style="background-color: lime; font-size: large;">0</span></div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;"></span></div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;">Hence 1111 --&gt; 1010</span><br /> <br /> <span style="background-color: white;">Lets try one more example:-</span><br /> <br /> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">Gray Code&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Conversion &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Binary Code</span></div> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">&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; G<span style="font-size: x-small;">msb+1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span style="font-size: large;">B<span style="font-size: x-small;">msb</span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: red; font-size: large;">0</span><span style="font-size: large;">101&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;"><span style="background-color: white;"><span style="background-color: red;">0</span> &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; <span style="background-color: red;">0<span style="background-color: white;"> </span><span style="background-color: white;">&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; </span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">0</span></span><span style="background-color: lime; font-size: large;">1</span><span style="font-size: large;">01&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: lime; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp; &nbsp;&nbsp;</span><span style="font-size: large;">&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; <span style="background-color: white;">0</span></span><span style="background-color: lime; font-size: large;"><span style="background-color: lime;">1</span><span style="background-color: white;"> &nbsp;&nbsp;&nbsp;&nbsp; </span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">01</span></span><span style="background-color: blue; font-size: large;">0</span><span style="font-size: large;">1&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">0</span><span style="font-size: large;"> &nbsp;&nbsp;&nbsp; +&nbsp;&nbsp;&nbsp; </span><span style="background-color: lime; font-size: large;">1</span><span style="font-size: large;">=&nbsp;&nbsp; <span style="background-color: red;">1</span>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">0</span><span style="font-size: large;">1</span><span style="background-color: red; font-size: large;">1<span style="background-color: white;"> &nbsp;&nbsp; </span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">010</span></span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp; +&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">= 1</span><span style="background-color: lime; font-size: large;">0</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">011</span><span style="background-color: lime; font-size: large;">0</span></div> <span style="background-color: white;">*</span><span style="background-color: red; font-size: large;"><span style="background-color: white;"><span style="background-color: red;"><span style="background-color: white;">(0 is not a significant digit)</span></span></span></span><span style="background-color: white;"> </span><br /> <span style="background-color: white;">Hence 0101 --&gt;0110</span></div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;">Try same for:</span></div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;">Gray Code &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Binary Code</span></div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;">&nbsp;&nbsp;&nbsp; 0000&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; </span>0000</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0001&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; 0001</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0010&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; 0011</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0011&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; 0010</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0100&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; 0111</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 0101 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0110</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 0110 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0100</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 0111 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0101</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1000 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1111</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1001 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1110</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1010&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1100</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 1011&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1101</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1100 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1000</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1101 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1001</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1110 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1011</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1111 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1010</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <br /> <b>Now we will convert a Binary-coded number to Gray by following method :-</b> <br /> <br /> The binary number and the Gray-coded number will have the same number of bits.<br /> <br /> 1. Gray MSB (most significant bit) i.e left most and Binary MSB will be same.<br /> <br /> 2. To get Gray next to MSB (next digit to the right) subtract next MSB(to right) of Binary from its MSB.<br /> &nbsp;B<span style="font-size: x-small;">msb </span>- B<span style="font-size: x-small;">msb+1</span>=G<br /> <br /> 3. Ignore negative sign.<br /> <br /> 4. Continue through this manner right through the end <br /> <br /> example:- <br /> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">Binary Code&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Conversion &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Gray Code</span></div> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">&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; B<span style="font-size: x-small;">msb &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span style="font-size: large;"><span style="font-size: x-small;"><span style="font-size: large;">B</span>msb+1</span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">111&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;"><span style="background-color: white;"><span style="background-color: red;">1</span>&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; <span style="background-color: red;">1<span style="background-color: white;">&nbsp;</span><span style="background-color: white;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)</span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: blue; color: black; font-size: large;">1</span><span style="background-color: red; color: black; font-size: large;">1</span><span style="font-size: large;"><span style="background-color: white;">11</span>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp; &nbsp; - &nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">=&nbsp;&nbsp; </span><span style="background-color: lime; font-size: large;">0</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: lime; font-size: large;"><span style="background-color: white;">1</span>0<span style="background-color: white;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2), (3)</span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">1<span style="background-color: blue;">1</span></span></span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">1&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp; - &nbsp; &nbsp; </span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">=&nbsp;&nbsp; <span style="background-color: lime;">0</span> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">1</span><span style="background-color: white; font-size: large;">0</span><span style="background-color: red; font-size: large;"><span style="background-color: lime;">0</span><span style="background-color: white;"> &nbsp;&nbsp;&nbsp; (4)</span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">11<span style="background-color: blue;">1</span></span></span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp; -&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">= &nbsp; </span><span style="background-color: lime; font-size: large;">0</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">1</span><span style="background-color: white; font-size: large;">0</span><span style="background-color: white; font-size: large;">0</span><span style="background-color: lime; font-size: large;">0</span></div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;">Hence 1111 --&gt; 1000</span><br /> <br /> <span style="background-color: white;">Here we try one more example :-&nbsp;</span><br /> <span style="background-color: white;"><br /></span><br /> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">Binary Code&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Conversion &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Gray Code</span></div> <div style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;">&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; B<span style="font-size: x-small;">msb &nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <span style="font-size: large;"><span style="font-size: x-small;"><span style="font-size: large;">B</span>msb+1</span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: red; font-size: large;">0</span><span style="font-size: large;">101&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;"><span style="background-color: white;"><span style="background-color: red;">0</span> &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; <span style="background-color: red;">0<span style="background-color: white;"> </span><span style="background-color: white;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white; color: black; font-size: large;">0</span><span style="background-color: blue; color: black; font-size: large;">1</span><span style="font-size: large;"><span style="background-color: white;">01</span>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp; &nbsp;&nbsp;</span><span style="font-size: large;">&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; </span><span style="background-color: lime; font-size: large;"><span style="background-color: white;">0</span>1<span style="background-color: white;"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">0<span style="background-color: blue;">1</span></span></span><span style="background-color: red; font-size: large;">0</span><span style="font-size: large;">1&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: blue; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp;&nbsp; - &nbsp; &nbsp; </span><span style="background-color: red; font-size: large;">0</span><span style="font-size: large;">=&nbsp;&nbsp; <span style="background-color: lime;">1</span> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">01</span><span style="background-color: white; font-size: large;"></span><span style="background-color: red; font-size: large;"><span style="background-color: lime;">1</span><span style="background-color: white;"> &nbsp;&nbsp;&nbsp; </span></span></div> <div style="color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="font-size: large;"><span style="background-color: white;">01<span style="background-color: blue;">0</span></span></span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; </span><span style="background-color: blue; font-size: large;">0</span><span style="font-size: large;"> &nbsp;&nbsp;&nbsp; -&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: red; font-size: large;">1</span><span style="font-size: large;">= &nbsp; </span><span style="background-color: lime; font-size: large;">1</span><span style="font-size: large;"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span style="background-color: white; font-size: large;">011</span><span style="background-color: white; font-size: large;"></span><span style="background-color: lime; font-size: large;">1</span></div> <span style="background-color: white;">Hence 0101 --&gt;0111</span><br /> <br /> <span style="background-color: white;">Try some more:-</span><br /> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;">Binary Code &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp; Gray Code</span></div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> <span style="background-color: white;">&nbsp;&nbsp;&nbsp; 0000&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; </span>0000</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0001&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; 0001</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0010&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; 0011</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0011&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; 0010</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 0100&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; 0110</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 0101 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0111</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 0110 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0101</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 0111 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; 0100</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1000 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1100</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1001 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1101</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1010&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1111</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp;&nbsp;&nbsp; 1011&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1110</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1100 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1010</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1101 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1011</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1110 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1001</div> <div style="background-color: white; color: black; font-family: Arial,Helvetica,sans-serif;"> &nbsp; &nbsp; 1111 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1000</div> </div> </div> </div>satpanhttp://www.blogger.com/profile/02844676451849547823noreply@blogger.com1