Lecture 2 - Introduction to Logic Gates

CSSE2010

Digital Logic

Only two logical levels present (i.e. binary)

• Logic “0” - where usually small voltages (around 0 volts) occur
• Logic “1” - where usually larger voltage (around 0.8 to 5 volts, depending on the “logic family”, i.e. transistors) occur.

Logic Gates

Logic Gates are the building blocks of computers, where each gate has one or more inputs, and always have one output. These Logic Gates perform logic operations (or functions) that consist of 7 basic types:

1. NOT
2. AND
3. OR
4. NAND
5. NOR
6. XOR
7. XNOR Inputs and outputs can really only have two states: 1 & 0. This can also be expressed as “true” and “false”.

![[Pasted image 20240229135015.png|XOR is the odd function and XNOR is the even function. When $A+B=2k$ where $k\in \mathbb{Z}$, then TRUE.]]

Boolean Logic Functions

Logic functions can be expressed as expressions involving variables (such as $A,B,C,\dots ,Z$), and functions (such as $+,\cdot ,\circ$).

Rules about how this works are called Boolean algebra. Variables and functions can only take on values of 0 or 1.