Final answer:
The digital circuit for the function f(a,b,c,d)= Σm(1,3,6,9,12,13) is designed by minimizing Boolean expressions for minterms and using these expressions to create optimized 2-level and 3-level circuits with AND and OR gates.
Step-by-step explanation:
To design a digital circuit that implements the function f(a,b,c,d)= Σm(1,3,6,9,12,13), we first need to find the minimized form of the function using a Karnaugh map (K-map) or Quine-McCluskey algorithm.
We identify the Boolean expressions for the minterms and then simplify them using Boolean algebra to obtain the most optimized 2-level and 3-level circuits using AND and OR gates.
For a 2-level circuit, we seek to minimize the number of gates and inputs per gate. We could aim for the Sum of Products form, where we OR the ANDed minterms.
For a 3-level circuit, we might use a combination of AND, OR, and NOT gates for further simplification, possibly incorporating the NAND or NOR logic as intermediate stages if they provide simplification benefits.
Upon completing the simplification, we'll have two Boolean expressions representing the 2-level and 3-level circuits. These expressions will then be used to draw the final circuit diagrams, ensuring that each gate and connection reflects the simplified logic for function f.
It's important to note that while building the circuit, attention must be given to the logical representation of each level and the minimization of components used.