Final answer:
To realize Z using only two-input NAND gates, we can apply De Morgan's laws to transform the given function into a form that uses only NAND operations. We start by complementing the original function, converting it to NAND form, and then taking a complement of the resultant expression using NAND gates. The implementation requires converting triple-input NAND equivalents into forms that use two-input NAND gates and employing gate sharing to minimize the number of gates.
Step-by-step explanation:
To realize the function Z = ABC + AD + C'D' using only two-input NAND gates, we first need to understand that a NAND gate is a universal gate, meaning it can be used to implement any Boolean function. The given function needs to be converted into a form that only uses NAND operations. This can be achieved by applying De Morgan's laws and using the fact that a NAND gate can also implement NOT, AND, and OR functions with appropriate connections.
The expression provided is already in a form that appears close to NAND-only implementation. However, we need to transform it into an equivalent expression that uses NAND gates. To achieve this, we can take the complement of the entire function and then take the complement of the resulting expression, effectively cancelling the double complement and leaving the original function unchanged (since NOT(NOT(Z)) = Z).
Here is a step-by-step transformation of the function using NAND gates:
- Step 1: Take the complement of the original function: Z' = (ABC)'(AD)'(C'D')'.
- Step 2: Convert to NAND form by using the NAND equivalents: Z' = (A NAND B NAND C)(A NAND D)(C NAND D).
- Step 3: Take the complement of Z' to get Z by using a single NAND gate: Z = Z' NAND Z'.
This implementation simplifies the original function using only NAND gates. It is important to note that the actual implementation would require the expansion of the triple-input NAND equivalent using two-input NAND gates, which adds more steps to the process. A minimalistic approach should always consider the ability to share common sub-expressions to reduce the number of gates used.