Lecture 1-2: Principles of combinational logics (con't)

We studied the Boolean expression in terms of Sum of Products (SoP) and Product of Sums (PoS). Moreover, we also learnt Boolean Algebra postulates and theorem used to simplify Boolean expressions.

Karnaugh map was introduced as a useful method to simplify/optimize any Boolean expression.

Lab 1 - Get used with digital logic gates using with Circuit Maker software

In the first lab, we are going to get used with the Circuit Marker 2000 software. 

How to use this software: https://eng3380.blogspot.ca/p/circuit-maker-how-to-use.html

Using this software to do the following lab assignments:

1. Using AND, OR, NOT logic gates to build up and evaluate the following circuits

1a. A 2-input NAND gate
1b. A 2-input NOR gate
1c. A 2-input XOR gate
1d. A 2-input XNOR gate
1f. A 3-input NAND gate
1g. A 3-input NOR gate
1h. A 3-input XOR gate
1i. A 3-input XNOR gate

2. Build a Binary to Decimal (BCD) circuit
Build up Binary-Coded Decimal (BCD) converter using 7 primitive logic gates

Using the following steps to build up a BCD converter circuit.
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 outputs (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.

If you do it well, please continue your next lab with a new convertor named Binary to 7 Segment Display

Lecture 1-2: Principles of combinational logics

We studied 7 basic logic gates. We concluded that using only AND, OR, NOT (AIO), we can build any functional digital circuits.

We studied the Boolean algebra to find out how to find an Boolean expression from a given truth table. 

Lecture 1-1 Number Systems and Codes

We learnt about the number systems including Decimal, Binary, Hexadecimal, Oct. More importantly, we studied how to convert one number system to another number system, and vice versa, using the formal polynomial representation

We studied the characteristic feature of number system theory - Complement. We mostly played with the Binary number system to find out how to use the complement to represent negative number and its sign, which are triggered using digital logic components to perform arithmetic operations. We also learned that, using 2's complement, we can subtraction to addition operation only.

We move on to code systems. Using the Binary system, we can encode data in terms of binary combinations, which are used for various daily life applications.