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Number Conversion from one
system to another
➔ Types of code:
1. Weighted codes
2. Non-Weighted codes
3. Reflective codes
4. Sequential codes
5. Alphanumeric codes
6. Error Detection & correcting
codes
Binary to Gray:
● Invented by Frank Gray.
● Unweighted code.
● Also known as Reflected Binary
Code(RBC).
● Two successive value differs
only by one bit. It reduces
switching operation.
● Use in a K-map.
Binary conversion to Gray conversion
Step 1: Record the 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.
Gray code to Binary code conversion
Step 1:Record the MSB as it is.
Step 2:Add to the next bit if Gray code,record
the sum and neglect the carry.
Step 3:Repeat the process.
Circuit diagram:
Binary coded decimal(BCD)
● In this code each decimal
digit is represented by a 4-bit
binary number.
● Positional weights are
8-4-2-1.
● BCD is less efficient than
Binary.
Conversion of Decimal to
BCD
Example:
1. 17 ==>00010111
2. 156 ==>000101010110
3. 30 ==>00110000
Conversion of BCD to Decimal
Example:
1.00011001==>19
2.01000101==>45
3.01010100==>54
25
35
22
Excess-3
● Xs-3 or X-3 code is unweighted
code.
● 4-bit code.
Circuit diagram : BCD to Excess-3
Digital Code conversion from one system to another.

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Digital Code conversion from one system to another.

  • 1. Number Conversion from one system to another
  • 2. ➔ Types of code: 1. Weighted codes 2. Non-Weighted codes 3. Reflective codes 4. Sequential codes 5. Alphanumeric codes 6. Error Detection & correcting codes
  • 3. Binary to Gray: ● Invented by Frank Gray. ● Unweighted code. ● Also known as Reflected Binary Code(RBC). ● Two successive value differs only by one bit. It reduces switching operation. ● Use in a K-map.
  • 4. Binary conversion to Gray conversion Step 1: Record the 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.
  • 5. Gray code to Binary code conversion Step 1:Record the MSB as it is. Step 2:Add to the next bit if Gray code,record the sum and neglect the carry. Step 3:Repeat the process.
  • 7. Binary coded decimal(BCD) ● In this code each decimal digit is represented by a 4-bit binary number. ● Positional weights are 8-4-2-1. ● BCD is less efficient than Binary.
  • 8. Conversion of Decimal to BCD Example: 1. 17 ==>00010111 2. 156 ==>000101010110 3. 30 ==>00110000 Conversion of BCD to Decimal Example: 1.00011001==>19 2.01000101==>45 3.01010100==>54 25 35 22
  • 9. Excess-3 ● Xs-3 or X-3 code is unweighted code. ● 4-bit code.
  • 10. Circuit diagram : BCD to Excess-3