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Code conversions binary to Gray vice versa.pptx

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Ramakrishna Reddy Bijjam
Ramakrishna Reddy Bijjam

Code Conversions Binary code to gray code and gray code to binary conversion Weighted and non weighted conversions

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Group: MCA I Year Subject: Computer Architecture Semester: I AVANTHI PG COLLEGE, Hyderabad
Topic: Code conversions
The digital data is represented, stored and transmitted as group of binary bits. This group is also called as binary code. The binary code is represented by the number as well as alphanumeric letter. What is meant by code? Codes are classified in to 2 types Weighted Non-weighted
In weighted code, each digit position has a weight or value. The sum of all digits multiplied by a weight gives a total amount being represented. BCD or 8421 is a type of weighted code where each digit position is assigned a specific weight. WEIGHTED CODE
In non weighted code there is no positional weight i.e., Each position within the binary number is not assigned a prefix value. No specific positions are assigned to bit positions in non weighted code. The non weighted codes are (1) Gray code (2) Excess-3 code. NON WEIGHTED CODE
Code converters Some of the conversions are Code conversion is used to change the data present in one type of binary code to another type of binary code. Some of the codes are BCD, Gray, Excess 3, ASCII and so on. Binary to Gray code conversion Gray to Binary code conversion BCD to Excess-3 code conversion Excess-3 to BCD code conversion
The Gray code is non-weighted code, as the position of bit does not contain any weight. The Gray code is a reflective digital code which has the special property that any two subsequent numbers codes differ by only one bit. This is also called a unit- distance code. Binary to Gray code conversion
The generation of 4-bit Gray code can be calculated by using formula. G1 = B1 G2 = B1B2 G3 = B2B3 G4 = B3B4
The most significant bit (MSB) of the Gray code is always equal to the MSB of the given binary code other bits of the output Gray code can be obtained by Xoring binary code bit at that index and previous index. The binary to Gray code conversions can be done by using xoring logic gate. A four-bit binary code converter is shown above. The input is binary code and the output is equivalent Gray code.
A four-bit binary to Gray code conversion table is as shown below. Four Bit Binary Number Four Bit Gray Code B1 B2 B3 B4 G1 G2 G3 G4 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1
The circuit for Binary to Gray code conversion is
Gray to binary code conversion In Gray to binary conversion, the input is Gray code and output is its equivalent binary code. The generation of four-bit binary equivalent code can be calculated by using formula. B1 = G1 B2 = G2 B1 B3 = G3 B2 B4 = G4 B3
The MSB of binary code is similar to the MSB of Gray code. To get next bit, use the xoring operation among the MSB of binary to the next bit of the Gray code. Similarly, to get the third bit, it uses the xoring operation among the second bit to the third MSB of the Gray code and so on.
The Gray to binary conversion method can be done by using xoring logic gate. A four-bit Gray to binary code converter is as shown below.
Four Bit Gray Code Four Bit Binary Number G1 G2 G3 G4 B1 B2 B3 B4 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 A four-bit Gray to binary code conversion table is as shown below.
BCD to Excess 3 code Excess-3 codes are unweighted and can be obtained by adding 3 to each decimal digit then it can be represented by using 4-bit binary number for each digit. To find the decimal equivalent of the given binary number. Add 0011 to each four-bit group in binary coded decimal number (BCD) to get desired excess-3 equivalent. The variables B0, B1, B2, and B3 represent the bits of the binary numbers. The variable 'B0' represents the LSB, and the variable 'B3' represents the MSB. The variables E0, E1, E2, and E3 represent the bits of the Excess-3 code. The variable 'E0' represents the LSB, and the variable 'E3' represents the MSB.
The truth table for BCD to Excess-3 code converter can be determined as shown in table below. For impossible four bit Excess-3 code we use output as Dont care conditions. The 'don't care conditions' is defined by the variable 'X'. BCD Number Excess-3 Code Number Decimal B3 B2 B1 B0 E3 E2 E1 E0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0 0 1 0 0 1 0 1 3 0 0 1 1 0 1 1 0 4 0 1 0 0 0 1 1 1 5 0 1 0 1 1 0 0 0 6 0 1 1 0 1 0 0 1 7 0 1 1 1 1 0 1 0 8 1 0 0 0 1 0 1 1 9 1 0 0 1 1 1 0 0
The circuit diagram for BCD to Excess-3 code converter is shown below
Excess-3 to BCD converter The process of converting Excess-3 to BCD is opposite to the process of converting BCD to Excess-3. The BCD code can be calculated by subtracting 3, i.e., 0011 from each four- digit Excess-3 code. The variables E0, E1, E2, and E3 represent the bits of the Excess-3 code. The variable 'E0' represents the LSB, and the variable 'E3' represents the MSB. The variables B0, B1, B2, and B3 represent the bits of the binary numbers. The variable 'B0' represents the LSB, and the variable 'B3' represents the MSB. The 'don't care conditions' is defined by the variable 'X'.
The circuit diagram for Excess-3 code to BCD converter is shown below
The truth table for BCD to Excess-3 code converter can be determined as shown in table below. Excess-3 Code Number BCD Number Decimal E3 E2 E1 E0 B3 B2 B1 B0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 2 0 1 0 1 0 0 1 0 3 0 1 1 0 0 0 1 1 4 0 1 1 1 0 1 0 0 5 1 0 0 0 0 1 0 1 6 1 0 0 1 0 1 1 0 7 1 0 1 0 0 1 1 1 8 1 0 1 1 1 0 0 0 9 1 1 0 0 1 0 0 1
PREPARED BY RAMAKRISHNA REDDY BIJJAM AVANTHI PG COLLEGE HYDERABAD

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Code conversions binary to Gray vice versa.pptx

  • 1. Group: MCA I Year Subject: Computer Architecture Semester: I AVANTHI PG COLLEGE, Hyderabad
  • 3. The digital data is represented, stored and transmitted as group of binary bits. This group is also called as binary code. The binary code is represented by the number as well as alphanumeric letter. What is meant by code? Codes are classified in to 2 types Weighted Non-weighted
  • 4. In weighted code, each digit position has a weight or value. The sum of all digits multiplied by a weight gives a total amount being represented. BCD or 8421 is a type of weighted code where each digit position is assigned a specific weight. WEIGHTED CODE
  • 5. In non weighted code there is no positional weight i.e., Each position within the binary number is not assigned a prefix value. No specific positions are assigned to bit positions in non weighted code. The non weighted codes are (1) Gray code (2) Excess-3 code. NON WEIGHTED CODE
  • 6. Code converters Some of the conversions are Code conversion is used to change the data present in one type of binary code to another type of binary code. Some of the codes are BCD, Gray, Excess 3, ASCII and so on. Binary to Gray code conversion Gray to Binary code conversion BCD to Excess-3 code conversion Excess-3 to BCD code conversion
  • 7. The Gray code is non-weighted code, as the position of bit does not contain any weight. The Gray code is a reflective digital code which has the special property that any two subsequent numbers codes differ by only one bit. This is also called a unit- distance code. Binary to Gray code conversion
  • 8. The generation of 4-bit Gray code can be calculated by using formula. G1 = B1 G2 = B1B2 G3 = B2B3 G4 = B3B4
  • 9. The most significant bit (MSB) of the Gray code is always equal to the MSB of the given binary code other bits of the output Gray code can be obtained by Xoring binary code bit at that index and previous index. The binary to Gray code conversions can be done by using xoring logic gate. A four-bit binary code converter is shown above. The input is binary code and the output is equivalent Gray code.
  • 10. A four-bit binary to Gray code conversion table is as shown below. Four Bit Binary Number Four Bit Gray Code B1 B2 B3 B4 G1 G2 G3 G4 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1
  • 11. The circuit for Binary to Gray code conversion is
  • 12. Gray to binary code conversion In Gray to binary conversion, the input is Gray code and output is its equivalent binary code. The generation of four-bit binary equivalent code can be calculated by using formula. B1 = G1 B2 = G2 B1 B3 = G3 B2 B4 = G4 B3
  • 13. The MSB of binary code is similar to the MSB of Gray code. To get next bit, use the xoring operation among the MSB of binary to the next bit of the Gray code. Similarly, to get the third bit, it uses the xoring operation among the second bit to the third MSB of the Gray code and so on.
  • 14. The Gray to binary conversion method can be done by using xoring logic gate. A four-bit Gray to binary code converter is as shown below.
  • 15. Four Bit Gray Code Four Bit Binary Number G1 G2 G3 G4 B1 B2 B3 B4 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 A four-bit Gray to binary code conversion table is as shown below.
  • 16. BCD to Excess 3 code Excess-3 codes are unweighted and can be obtained by adding 3 to each decimal digit then it can be represented by using 4-bit binary number for each digit. To find the decimal equivalent of the given binary number. Add 0011 to each four-bit group in binary coded decimal number (BCD) to get desired excess-3 equivalent. The variables B0, B1, B2, and B3 represent the bits of the binary numbers. The variable 'B0' represents the LSB, and the variable 'B3' represents the MSB. The variables E0, E1, E2, and E3 represent the bits of the Excess-3 code. The variable 'E0' represents the LSB, and the variable 'E3' represents the MSB.
  • 17. The truth table for BCD to Excess-3 code converter can be determined as shown in table below. For impossible four bit Excess-3 code we use output as Dont care conditions. The 'don't care conditions' is defined by the variable 'X'. BCD Number Excess-3 Code Number Decimal B3 B2 B1 B0 E3 E2 E1 E0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1 0 0 2 0 0 1 0 0 1 0 1 3 0 0 1 1 0 1 1 0 4 0 1 0 0 0 1 1 1 5 0 1 0 1 1 0 0 0 6 0 1 1 0 1 0 0 1 7 0 1 1 1 1 0 1 0 8 1 0 0 0 1 0 1 1 9 1 0 0 1 1 1 0 0
  • 18. The circuit diagram for BCD to Excess-3 code converter is shown below
  • 19. Excess-3 to BCD converter The process of converting Excess-3 to BCD is opposite to the process of converting BCD to Excess-3. The BCD code can be calculated by subtracting 3, i.e., 0011 from each four- digit Excess-3 code. The variables E0, E1, E2, and E3 represent the bits of the Excess-3 code. The variable 'E0' represents the LSB, and the variable 'E3' represents the MSB. The variables B0, B1, B2, and B3 represent the bits of the binary numbers. The variable 'B0' represents the LSB, and the variable 'B3' represents the MSB. The 'don't care conditions' is defined by the variable 'X'.
  • 20. The circuit diagram for Excess-3 code to BCD converter is shown below
  • 21. The truth table for BCD to Excess-3 code converter can be determined as shown in table below. Excess-3 Code Number BCD Number Decimal E3 E2 E1 E0 B3 B2 B1 B0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 1 2 0 1 0 1 0 0 1 0 3 0 1 1 0 0 0 1 1 4 0 1 1 1 0 1 0 0 5 1 0 0 0 0 1 0 1 6 1 0 0 1 0 1 1 0 7 1 0 1 0 0 1 1 1 8 1 0 1 1 1 0 0 0 9 1 1 0 0 1 0 0 1
  • 22. PREPARED BY RAMAKRISHNA REDDY BIJJAM AVANTHI PG COLLEGE HYDERABAD