Logic Gates

• A technique for implementing Boolean function using logic gates
• Logic gates:
  1. Elementary (Nand, And , Or, Not…)
  2. Composite (Mux, Adder,….)

Elementary Logic Gates

NAND

Gate Diagram:

Function specification:

if (a==1 and b==1)
then out=0 else out=1

Truth Table

Circuit implementation

The following course does not deal with physical implementation of gates

• Circuits, transistors, relays, etc is part of Electrical Engineering and not computer science.

Hardware Simulator

Nand give is an elementary gate already provided in the course so no implementation need for this, we will build all other gates using Nand Gates.

Building logic gates and chips in a structured and incremental manner is crucial in a course like nand2tetris, where each component builds upon the functionality of previously constructed ones. Below is a recommended sequence for building the listed gates and chips, starting with the simplest and moving towards the more complex. This order ensures that each component you build can be tested and used in the subsequent, more complex components.

Recommended Order for Building Gates and Chips:

1. Not

   • Start with the Not gate, as it is the simplest modification of a Nand gate and is fundamental to building other logic gates.

2. And

   • Next, construct the And gate using the Nand and Not gates. The And gate forms a basic building block for many other chips.

3. Or

   • Build the Or gate using Nand gates, which will also utilize the Not gate. The Or gate is essential for creating the Xor gate and various multiplexers.

4. Xor

   • With Nand, Not, and Or gates at your disposal, you can now construct the Xor gate, which is slightly more complex and used in various computing functions.

5. Mux

   • The basic Mux (Multiplexer) can be built using And, Or, and Not gates. This component is foundational for creating more complex multiplexers.

6. Dmux

   • Construct the Dmux (Demultiplexer) next, using previously built gates like Not and And. This chip is crucial for distributing signals in circuits.

7. Not16

   • Construct the Not16 gate, which extends the functionality of the Not gate to 16-bit inputs. This requires simply replicating the Not operation across 16 channels.

8. And16

   • Similarly, build the And16 gate, which is an extension of the And gate to 16-bit inputs.

9. Or16

   • Follow with Or16, which is an extension of the Or gate to handle 16-bit inputs.

10. Or8Way

    • The Or8Way takes an 8-input and outputs true if any input is true. This can be built using the Or and Or16 logic.

11. Mux16

    • Build the Mux16, which is a 16-bit version of the Mux, using 16 sets of Mux gates to handle 16-bit inputs.

12. Mux4Way16

    • This is a 4-way 16-bit multiplexer, and can be built using multiple Mux16 gates, controlled by additional logic gates to select among the 4 inputs.

13. Mux8Way16

    • Construct the Mux8Way16 using Mux4Way16 and other necessary logic components to expand the selection capability.

14. Dmux4Way

    • Build the Dmux4Way, a more complex version of the Dmux, using additional Dmux and logic gates to distribute a single input to one of four outputs.

15. Dmux8Way

    • Finally, construct the Dmux8Way, which extends the Dmux4Way functionality to eight outputs. This involves additional layers of demultiplexing.

Building Approach:

Each gate or chip should be fully tested before proceeding to build more complex components that depend on it. Use the testing scripts provided by nand2tetris to ensure each component works correctly according to the specifications. This order of building ensures a logical progression, making debugging easier and helping solidify your understanding of digital logic as each new component introduces additional complexity.