Advanced Digital Electronics
An innovative Tecxskills to the functions of modern digital electronics and computing architectures, from simple bits to complex finite state machines.
01. Digital Basics
Number Systems & Codes
The foundation of digital systems relies on Binary (Base-2), Octal (Base-8), and Hexadecimal (Base-16). Beyond raw values, we use Gray Code for error-free transitions and BCD for human-readable formats.
Binary: 1010(2)
Hex: 0xA(16)
Decimal: 10(10)
Arithmetic & Overflow
Arithmetic is performed using 2’s Complement logic. Overflow occurs when the result of an operation exceeds the range of the given bit-width.
- Unsigned Range: 0 to 2n-1
- Signed Range: -2n-1 to 2n-1-1
- Detection: Cin XOR Cout of MSB
02. Boolean Algebra
Fundamental Laws
- Commutative: A + B = B + A
- Associative: (A+B)+C = A+(B+C)
- Distributive: A(B+C) = AB + AC
- Identity: A + 0 = A
DeMorgan’s Theorem
¬(A ∧ B) = ¬A ∨ ¬B
¬(A ∨ B) = ¬A ∧ ¬B
Minimization
Using Karnaugh Maps (K-Maps) to reduce gate counts. Essential for minimizing propagation delay and power consumption in physical silicon.
03. Logic Gates
Y = A ⋅ B
Y = A + B
Universal
Y = A ⊕ B
04. Logic Examples & Truth Tables
Example: Half Adder Logic
A circuit to add two single binary bits.
| A | B | Sum (⊕) | Carry (⋅) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Functional minimization
Converting an expression to its simplest form:
F = BC(A’ + A) + ABC’
F = BC(1) + ABC’
F = BC + ABC’
// Minimal Form Found
05. Combinational Circuits
Arithmetic Circuits
Adders (Half/Full), Subtractors, and Look-Ahead Carry Generators for high-speed computation.
Data Selectors
Multiplexers (MUX) for routing and Demultiplexers for distribution.
Priority Encoders
Handling multiple inputs simultaneously by assigning hierarchy. Crucial for Interrupt Controllers in CPUs.
06. Sequential Circuits
Flip-Flops
The basic memory unit. Types: SR (Latch), JK (Universal), D (Data), and T (Toggle) Flip-Flops.
Race Conditions
Occurs in JK flip-flops when J=1, K=1 and clock pulse is too long. Solved via Edge-triggering or Master-Slave.
Sync Logic
Governed by a global Clock pulse to prevent glitch propagation across the circuit.
07. Registers & Counters
Shift Registers
Operations: Shift-Left / Shift-Right
FSM (Finite State Machines)
Mathematical models for sequential logic controllers.
08. Families & Converters
Comparison of Logic Families
| Parameter | TTL | CMOS | ECL |
|---|---|---|---|
| Power Dissipation | 10mW | 0.01mW (Static) | 40-55mW |
| Prop. Delay | 10ns | 30-50ns | 1-2ns |
| Fan-out | 10 | 50+ | 25 |
ADC / DAC
Quantization error is the primary factor in ADC precision. DACs often use Weighted-Resistor or R-2R ladder networks for conversion.
Memory
ROM is non-volatile (EPROM, Flash). RAM is volatile, with DRAM requiring periodic refreshing of capacitive charges.