Lecture 2-3 Memory and Storage

We learnt about memory and storage. We mainly emphasized on Caches and RAM. 

We studied memory, memory organization, memory addresses, and control operation on memory.

Mini-project 1 (Assignment 2) released!

Mini-project 1 has been released. Click on this. 

Note that: 

Deadline of project submission: Thursday 4:00pm, March 06 2025

Live Demo: Wed 11:30am March 07 2025 (Lecture time on Friday)

Lecture 2-2: Sequencial circuits

We have studied through the principle of sequential circuits and analysis. We discussed about the circuit operation in time-line.

The key component is delay and feedback.
- On each logic gate, a signal is delayed for a duration of time. Accumulated delay through a circuit may be long enough to cause troubles for the output but also give opportunities to build up the other kind of circuits.
- Feedback of a circuit is about how to connect the circuit's output to its input. This sequence looks like Recursion in Programming, allowing to memorize the output data for next stage.

Utimately, we introduced various Flip-Flops and their functions as the memory cells which are used to build the memory of the computer.

Lecture 2-1 Principals of Arithmetic Functions

We studied functional building blocks of arithmetic computation: Half-adder and full-adder. Using these blocks as functional cells, we can build up an array of interconnected cells to do addition of bit stream.

Thanks to the complement and fundamental functional circuits (XOR, Selector), we can build up an iterative array of full-adders to do both addition and subtraction, which is the key component for programable digital circuits.

Lab 3: Building up functional digital circuits

Use primitive digital logic circuits to build up the following circuits:

1. 3-to-8 line decoder 

2. 4-to-1 multiplexer

3. 8-to-1 multiplexer 

4. Gray-to-Binary Convertor

5. Binary-to-Gray Convertor

Topics to be reviewed for in-class test

Review

Lecture 1-1 Number systems and Codes

- How to convert from a number system to another number system, e.g. Decimal to Binary, Binary to Hexadecimal and vice versa

- What are codes and its applications?

Lecture 1-2: Principal of combinational logics

- 7 primitive logic gates and their Truth table.

- Boolean algebra: 

    - Postulates & theorems

    - How to build up Boolean expression from a given Truth table using SOP and POS

    - How to simplify Boolean expression using postulates & theorems

    - How to use Karnaugh map to simplify/optimize a Boolean expression

Lecture 1-3: Combinational logic circuit design

- 5 steps of design procedure

- Functional circuits including enabling, selecting, encoding, decoding, multiplexing

- Hierarchical principles

Exercises:

Review examples explained in the lectures

Lecture 1-3: Combinational Logic Circuit Design

We studied 5 steps of the design procedure of combinational logic circuit design: specification, formulation, optimization, technology mapping, and verification. 

The design procedure was explained through various examples of functional circuits such as encoders, decoders, multiplexers, demultiplexers, etc.

The key point of this lecture is about hierarchical structure where a complex functional circuit can be built up by using fundamental functional circuits and primitive components.

Lab 2: Development of Functional Building Blocks

Continuing the first lab, we continue with the following exercises:

1. 4-bit Binary to 1-Seven Segment LED Display using 7 primitive logic gates

2. 4-bit Binary to 1-Seven Segment LED Display using NAND gates only

3. 4-bit Binary to 1-Seven Segment LED Display using NOR gates only

4. 8-bit Binary to 3-Seven Segment LED Display

Note that, we already learn how to build up Binary-Coded Decimal (BCD) converter using 7 primitive logic gates using the following steps in the first lab: 

1. Derive a truth table of Binary-Coded Decimal. Note that you will have 10 inputs (0,1,2,3,4,5,6,7,8,9) and 4 inputs (X,Y,Z,W).
2. Write Boolean expressions for each output w.r.t inputs
3. Simplify the output functions by using either Boolean algebra postulates and theorem or K-map
4. Build up the circuit using Circuit Marker.