Main answer:
To design a logic circuit using NAND gates only that converts BCD (Binary Coded Decimal) code to Gray Code, you can follow these steps:
1. Understand BCD and Gray Code:
BCD is a coding system that represents decimal digits (0-9) using a 4-bit binary code. Gray Code is a binary code where successive values differ by only one bit.
2. Determine the truth table:
Create a truth table showing the BCD inputs and the corresponding Gray Code outputs. Since BCD has 4 bits and Gray Code also has 4 bits, the truth table will have 16 rows.
3. Simplify the Boolean expressions:
Using Karnaugh maps or Boolean algebra, simplify the Boolean expressions for each output bit based on the truth table.
4. Implement the circuit using NAND gates:
Use the simplified Boolean expressions to create the logic circuit using only NAND gates. Each output bit will have its own set of NAND gates.
Step-by-step explanation:
BCD (Binary Coded Decimal) is a coding system used to represent decimal digits (0-9) using a 4-bit binary code. Gray Code, on the other hand, is a binary code where successive values differ by only one bit. To convert BCD to Gray Code using only NAND gates, you need to follow a step-by-step process.
First, you should understand the concepts of BCD and Gray Code. BCD represents decimal digits in binary form, with each decimal digit represented by a 4-bit binary code. Gray Code, on the other hand, is a binary code where consecutive values differ by only one bit.
To design the logic circuit, you need to create a truth table that shows the BCD inputs and the corresponding Gray Code outputs. Since BCD has 4 bits and Gray Code also has 4 bits, the truth table will have 16 rows.
Next, you should simplify the Boolean expressions for each output bit based on the truth table. This can be done using Karnaugh maps or Boolean algebra. Simplifying the expressions will help reduce the complexity of the circuit.
Finally, you can implement the circuit using only NAND gates. Each output bit will have its own set of NAND gates. By connecting the inputs and outputs according to the simplified Boolean expressions, you will have a logic circuit that converts BCD code to Gray Code.
It's important to note that there may be multiple ways to design the circuit using only NAND gates. The specific design will depend on the simplification of the Boolean expressions and the arrangement of the gates.
I hope this explanation helps you understand how to design a logic circuit using NAND gates to convert BCD code to Gray Code. If you have any further questions, feel free to ask.