Design a Full Adder with minimum number of transistors minimum number of transistors

To design a Full Adder using the minimum number of transistors, we can break the problem down into a series of steps. A Full Adder has three inputs (A, B, and Cin) and two outputs (Sum and Cout).

1. Break Down the Problem

1. Identify the logic expressions:

   • Sum: $S = A \oplus B \oplus C_{in}$
   • Carry Out: $C_{out} = (A \cdot B) + (C_{in} \cdot (A \oplus B))$

2. Determine the required gates:

   • XOR gates for the Sum output.
   • AND and OR gates for the Carry Out output.

2. Relevant Concepts

• The standard Full Adder can be implemented using a combination of:
  • 2 XOR gates
  • 2 AND gates
  • 1 OR gate
• Each XOR gate requires 4 transistors, and each AND gate requires 6 transistors. The OR gate can be implemented with 6 transistors as well.

3. Analysis and Detail

Let's calculate the number of transistors:

1. Sum Calculation:

   • The Sum $S$:
     • First XOR (A, B): 4 transistors.
     • Second XOR (Result of first XOR, Cin): 4 transistors.
   • Total for Sum: $4 + 4 = 8$ transistors.

2. Carry Out Calculation:

   • The Carry Out $C_{out}$:
     • AND gate (A, B): 6 transistors.
     • Resulting XOR (A, B) needs another AND with Cin: 6 transistors for the second AND gate.
     • OR gate combining the results of both ANDs: 6 transistors.
   • Total for Carry Out: $6 + 6 + 6 = 18$ transistors.

4. Verify and Summarize

• Total transistors required:
  • For Sum: 8 transistors.
  • For Carry Out: 18 transistors.
  • Total: $8 + 18 = 26$ transistors.

Final Answer

The minimum number of transistors required to design a Full Adder is 26 transistors.