Final answer:
The design process for a 2-to-4 line decoder involves creating a truth table, deriving logical expressions for each output, and implementing the circuit using NOR or NAND gates. For NOR gates, outputs are active high, and for NAND gates, they are active low.
Step-by-step explanation:
The question requests the design of a 2-to-4 line decoder both with an enable input using NOR gates for outputs active high and enable active high, and using NAND gates for outputs active low and enable active low. Let's break down the design process into steps for each version.
NOR-based Decoder Design (Outputs Active High, Enable Active High)
Firstly, create the truth table for the 2-to-4 decoder considering the enable input. It will show which output should be high based on the two input bits and the enable input.
Using the truth table, derive the logical expression for each output. In this case, each output can be expressed as a NOR of various combinations of the inputs and their complements, also considering the enable input.
Implement these logical expressions using NOR gates. Remember that a NOR gate can also be used to create NOT and OR functions by using techniques such as looping inputs.
NAND-based Decoder Design (Outputs Active Low, Enable Active Low)
- Repeat the process of creating the truth table as done for the NOR-based design. Here, the outputs will be active low.
- For the NAND-based design, derive the logical expressions for each output. These will be in terms of NAND operations instead.
- Construct the actual decoder circuit using NAND gates, again taking advantage of the NAND gate's ability to perform NOT and AND operations through particular configurations.
Do remember that to create an inverting function with NAND gates (to simulate the NOT operation), you can connect both inputs of a single NAND gate to the same signal. For NOR gates, this is not necessary as NOR is an inverting operation by nature.