To implement the logic of a 3-input NOR gate using the available chips (7400, 7402, 7404, 7408, 7432, 7486), we first need to understand the functions of these chips and then determine how to create the NOR operation using a combination of these chips.

Available Chips:

1. 7400 - Quad 2-input NAND gate
2. 7402 - Quad 2-input NOR gate
3. 7404 - Hex inverter (NOT gate)
4. 7408 - Quad 2-input AND gate
5. 7432 - Quad 2-input OR gate
6. 7486 - Quad 2-input XOR gate

Goal: 3-input NOR Gate

The truth table for a 3-input NOR gate is as follows:

• F = 1 if X = 0, Y = 0, Z = 0
• F = 0 if any of X, Y, or Z is 1

This can be written as: $F = \overline{X + Y + Z}$ Where the "+" represents the logical OR operation.

Steps to Implement the 3-Input NOR Gate:

1. Step 1: Create a 3-input OR gate
   Since the available chips are 2-input gates, we can combine two 2-input OR gates (from the 7432 chip) to form a 3-input OR gate:

   • First, use a 2-input OR gate to calculate $X + Y$.
   • Then, use another OR gate to combine the result with $Z$, i.e., $(X + Y) + Z$.

2. Step 2: Invert the OR result
   After obtaining $X + Y + Z$, you can use the 7404 (NOT gate) to invert the result, creating the NOR function:

   • F = $\overline{X + Y + Z}$

Example Circuit Using the Available Chips:

• Use a 7432 chip for the OR gates:
  1. $A = X + Y$ (first OR gate from 7432)
  2. $B = A + Z = (X + Y) + Z$ (second OR gate from 7432)
• Use a 7404 chip to invert $B$:
  1. F = $\overline{B} = \overline{(X + Y + Z)}$

This provides the desired 3-input NOR gate.

Would you like more details on how to connect these components, or have any further questions?

Here are 5 related questions that may expand your understanding:

1. How does a 3-input NOR gate differ from a 2-input NOR gate in terms of behavior?
2. What other combinations of chips could be used to implement a 3-input NOR gate?
3. How would you implement a 4-input NOR gate using similar logic and available chips?
4. Can you simplify the 3-input NOR operation using only NAND gates (7400)?
5. How does the propagation delay of each gate type affect the performance of the circuit?

Tip: When designing digital circuits, always consider the propagation delay of each gate to ensure that the output is stable.