Gray Code.pptx

Gray Code.pptx

• 1.
  Prof. Neeraj Bhargava PoojaDixit Department of Computer Science, School of Engineering & System Sciences MDS UniversityAjmer, Rajasthan
• 2.
   Gray Codesystem is a binary number system in which two successive pair of numbers differs in only one bit.  It is also known as Reflected binary code. (RBC) or Cyclic code.  Binary no is converted to gray code to reduce switching operation.  Today gray code are widely used to facilitate the error correction in digital communications such as cable TV system.  It is unweighted code that means it does not depends on positional value of digit.  It is also called unit distance code or minimum error code.  It is used in applications in which the normal sequence of binary numbers generated by the hardware may produce an error or ambiguity during the transition from one number to the next.  So, the Gray code can eliminate this problem easily since only one bit changes its value during any transition between two numbers.
• 3.
   Verify howtwo successive pair of numbers differs in only one bit.  Now if we take an 3,4 decimal no as example and check how this number convert into binary and gray code.  Now lets see how many bits are changing in case of binary number.  So, here in binary conversion total 3 bits(b0,b1,b2) are changing while in gray code only 1 bit is changed. Decimal Binary Gray b3 b2 b1 b0 g3 g2 g1 g0 3 0 0 1 1 0 0 1 0 4 0 1 0 0 0 1 1 0
• 4.
  Decimal Binary Gray 00 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 2 0 0 1 0 0 0 1 1 3 0 0 1 1 0 0 1 0 4 0 1 0 0 0 1 1 0 5 0 1 0 1 0 1 1 1 6 0 1 1 0 0 1 0 1 7 0 1 1 1 0 1 0 0 8 1 0 0 0 1 1 0 0 9 1 0 0 1 1 1 0 1 10 1 0 1 0 1 1 1 1 11 1 0 1 1 1 1 1 0 12 1 1 0 0 1 0 1 0 13 1 1 0 1 1 0 1 1 14 1 1 1 0 1 0 0 1 15 1 1 1 1 1 0 0 0 16 1 0 0 0 0 1 1 0 0 0
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   Now ifwe take an 7,8 decimal no as example and check how this no convert into binary and gray code.  Now lets see how many bits are changing in case of binary number.  So, here in binary conversion total 4 bits(b0,b1,b2,b3) are changing while in gray code only 1 bit is changed.  that’s why gray code is also called unit distance code or switching operation is reduced in gray code. Decimal Binary Gray b3 b2 b1 b0 g3 g2 g1 g0 7 0 1 1 1 0 1 0 0 8 1 0 0 0 1 1 0 0
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  Step 1: Recordthe MSB as it is. Step 2: Add the MSB to the next bit, record the sum and neglect the carry. Step 3: Repeat the process Ex1: Convert 1 0 1 1 to Grey code. Solution: 1 0 1 1 1 1 1 0 MSB LSB + + + +
• 7.
   XOR Operation Note: in Gray code conversion MSB remain same. A B XOR 0 0 0 0 1 1 1 0 1 1 1 0
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  : Convert 11 1 0 to Grey code. Solution: 1 1 1 0 1 0 0 1 Q1. 1001 Q2. 1010 Q3. 1111 + + + + MSB LSB
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  Step 1: Recordthe MSB as it is. Step 2: Add the MSB to the next bit of gray code, record the sum and neglect the carry. Step 3: Repeat the process Ex1: Convert 1 1 1 0 to Grey code. Solution: 1 1 1 0 1 0 1 1 MSB LSB + + + +
• 10.
   AssignmentQuestion 1. 1100 2.1011 3. 1000 Ex1: Convert 1 0 0 1 to Grey code. Solution: 1 0 0 1 1 1 1 0 + + + +