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tags: Introduction to Digital System
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# Chapter 2-Boolean Algebra and Logic Gates
## Boolean Algebra
1. Operations
1. Two-Valued Boolean Algebra
2. Properties:
* ※Complement: F'
2. Boolean Functions
3. Canonical and Standard Form
1. Canonical Form
1. Minterms and Maxterms:
2. Expressions
1. Sum of Minterms: The minterms whose sum defines the Boolean function are those that give the 1's of the function in a truth table.
$f_1=x'y'z+xy'z'+xyz$
$f_2=x'yz+xy'z+xyz'+xyz$
2. Product of Maxterms:
$f_1'=x'y'z'+x'yz'+x'yz+xy'z+xyz'\\\Rightarrow f_1''=f_1=(x+y+z)(x+y'+z)(x+y'+z')(x'+y+z')(x'+y'+z)$
3. Boolean Algebraic Representation
1. Sum of Minterms: $\sum$
2. Product of Maxterms: $\prod$
5. Disadvantage: It requires each term to contain all variables.
2. Standard Forms

## Logic Gates
1. Gates
* Extension to Multiple Inputs: A gate can be extended to multiple inputs if its binary operation is commutative and associative such as AND and OR.
2. Positive and Negative Logic
3. Compositions of Logic Gates
## Integrated Circuits:
1. Levels of Integration
1. SSI: Small-Scale Integration Devices
2. MSI: Medium-Scale Integration Devices
3. LSI: Large-Scale Integration Devices
4. VLSI: Very Large-Scale Integration Devices
2. Digital Logical Family:
1. TTL(Transistor-Transistor Logic):Standard
2. ECL(Emitter-Coupled Logic): High-spaced
3. MOS(Metal-Oxide Semiconductor): High component density
4. CMOS(Complementary Metal-Oxide Semiconductor: Low power consumption
3. Parameters for Digital Logic Families
1. Fan-Out: The maximum number of ouputs driven by a single logic gate that don't impair the normal operation
2. Fan-In: The number of inputs available in a gate
3. Power Dissipation: Power consumption
4. Propagation Delay: The length of time taken for a signal to reach its destination.
4. EDA
1. Schematic Editor
2. HDL
3. Logic Synthesis
5. Physical Realization of a Digital Circuit
1. ASIC: Application-Specific Integrated Circuit
2. FPGA: Field-Programmable Gate Array
3. CPLD: Complex Programmable Logic Device

**Reference**
NCKUCSIE 1101_Introduction to Digital System
Digital Design With an Introduction to The Verilog HDL, VHDL and System Verilog 6/e by M.Morris Mano Michael D. Ciletti