Digital Electronics Page: Difference between revisions
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<table> | <table> | ||
<tr><td>Decimal</td><td>BCD</td><td>Excess-3</td></tr> | <tr><td>Decimal</td><td>BCD</td><td>Excess-3</td></tr> | ||
<tr><td>0</td><td>0000</td><td>0011<td></td> | <tr><td>0</td><td>0000</td><td>0011</td></td> | ||
<tr><td>1</td><td>0001</td><td>0100<td></td> | <tr><td>1</td><td>0001</td><td>0100</td></td> | ||
<tr><td>2</td><td>0010</td><td>0101<td></td> | <tr><td>2</td><td>0010</td><td>0101</td></td> | ||
<tr><td>3</td><td>0011</td><td>0110<td></td> | <tr><td>3</td><td>0011</td><td>0110</td></td> | ||
<tr><td>4</td><td>0100</td><td>0111<td></td> | <tr><td>4</td><td>0100</td><td>0111</td></td> | ||
<tr><td>5</td><td>0101</td><td>1000<td></td> | <tr><td>5</td><td>0101</td><td>1000</td></td> | ||
<tr><td>6</td><td>0110</td><td>1001<td></td> | <tr><td>6</td><td>0110</td><td>1001</td></td> | ||
<tr><td>7</td><td>0111</td><td>1010<td></td> | <tr><td>7</td><td>0111</td><td>1010</td></td> | ||
<tr><td>8</td><td>1000</td><td>1011<td></td> | <tr><td>8</td><td>1000</td><td>1011</td></td> | ||
<tr><td>9</td><td>1001</td><td>1100<td></td> | <tr><td>9</td><td>1001</td><td>1100</td></td> | ||
</table> | </table> | ||
Revision as of 23:09, 14 January 2023
Gray Codes
This is a technique where we convert number from binary to grays. We do this because Gray reduces the bits we need to change to get to the next number. e.g. changing from 2 to 3 decimal requires a 1 bit change.
| Decimal | BCD | Gray Code |
| 0 | 0000 | 0000 |
| 1 | 0001 | 0001 |
| 2 | 0010 | 0011 |
| 3 | 0011 | 0010 |
| 4 | 0100 | 0110 |
| 5 | 0101 | 0111 |
| 6 | 0110 | 0101 |
| 7 | 0111 | 0100 |
| 8 | 1000 | 1100 |
| 9 | 1001 | 1101 |
| 10 | 1010 | 1111 |
Excess-3 Codes
To get an excess-3 code of a decimal number simply add 3 to each decimal digit. And then we write the 4-bit binary number for each digit of the decimal number. We can find the excess-3 code of the given binary number by using the following steps:
- We find the decimal number of the given binary number.
- Then we add 3 in each digit of the decimal number.
- Now, we find the binary code of each digit of the newly generated decimal number.
We can also add 0011 in each 4-bit BCD code of the decimal number for getting excess-3 code.
| Decimal | BCD | Excess-3 |
| 0 | 0000 | 0011 |
| 1 | 0001 | 0100 |
| 2 | 0010 | 0101 |
| 3 | 0011 | 0110 |
| 4 | 0100 | 0111 |
| 5 | 0101 | 1000 |
| 6 | 0110 | 1001 |
| 7 | 0111 | 1010 |
| 8 | 1000 | 1011 |
| 9 | 1001 | 1100 |