4.2.2 Useful Logic Gates

TL;DR

Learn how to build AND and OR gates with many inputs using a chain or tree approach.

Transcript

On our to-do list from the previous section is figuring out how to build AND and OR gates with many inputs. These will be needed when creating circuit implementations using a sum-of-products equation as our template. Let’s assume our gate library only has 2-input gates and figure how to build wider gates using the 2-input gates as building blocks. ... Read More

Key Insights

• 🏛️ Building wide gates with many inputs is possible using the associative property of the AND, OR, and XOR operations.
• 🌲 The choice between chain and tree approaches depends on the cost and performance requirements of the circuit.
• 🧑‍🏭 Propagation delay is an important factor to consider in circuit design, as it affects the overall performance.
• 🔬 NAND and NOR gates are preferred in CMOS circuit design due to their single-gate implementation and better performance.
• 🔬 XOR gates require more components compared to NAND and NOR gates but are useful for arithmetic and parity calculations.
• 🔬 2-INPUT NAND and NOR gates are universal gates that can be used to implement sum-of-products circuits.

Questions & Answers

Q: How can we build AND and OR gates with many inputs using 2-input gates?

By utilizing the associative property of these operations, we can perform pair-wise operations in any order, allowing us to create wide gates.

Q: What is the difference between the chain and tree approach to building wide gates?

The chain approach involves connecting 2-input gates in a linear manner, while the tree approach creates a hierarchical structure with 2-input gates at each level.

Q: Which approach is better: chains or trees?

The choice depends on the desired cost and performance. Chains have linear propagation delay, while trees have logarithmic propagation delay with the number of inputs.

Q: What is the significance of propagation delay in circuit design?

Propagation delay measures the worst-case delay from inputs to outputs and affects the overall performance of the circuit.

Summary & Key Takeaways

• The associative property of the AND, OR, and XOR operations allows us to create wide gates by performing pair-wise operations in any order.

• There are two approaches to building wide gates: using a chain of 2-input gates or building a tree of 2-input gates.

• The choice between chains and trees depends on the desired cost and performance of the circuit.