Digital Electronics Cheat Sheet: Essential Logic Design

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3-Stage Carry Look Ahead Adder Using Basic Gates

• Carry Generate: G = A · B
• Carry Propagate: P = A ⊕ B
• C₁ = G₀ + P₀ · C_in
• C₂ = G₁ + P₁ · C₁
• C₃ = G₂ + P₂ · C₂
• Reduces delay by avoiding ripple carry.

Realization of Boolean Function Using MUX

(a) 4×1 MUX:

• Use 2 variables as select lines, rest for input logic.
• Map the output as per the truth table.

(b) 8×1 MUX:

• Use 3 variables as select lines.
• Directly assign data lines as per minterms.

Mealy vs. Moore State Machines

• Mealy: Output = f(state, input), faster response.
  Example: Sequence detector
• Moore: Output = f(state), more stable.
  Example: Traffic light controller

Full Adder Circuit in VHDL

Sum <= A XOR B XOR Cin;
Cout <= (A AND B) OR (Cin AND (A XOR B));

• Inputs: A, B, C_in
• Outputs: Sum, C_out

3-Bit Gray Code Synchronous Counter Using J-K FFs

• Gray sequence: 000 → 001 → 011 → 010 → 110 → 111 → 101 → 100
• Toggle control: Use K-map to derive J, K inputs.

Boolean Function Minimization Using K-Map

• Fill 1s for minterms.
• Group in 1, 2, 4, 8...
• Eliminate changing variables in groups.
• Derive SOP or POS.

Sequential Circuit with T Flip-Flops

• T = 1: Toggle
• Excitation table: Q(next) = T ⊕ Q(current)
• Draw state diagram first, then circuit.

Universal Shift Register

• Modes: Hold, Shift Right, Shift Left, Parallel Load
• Uses D Flip-Flops and MUX.
• Controlled by S₁, S₀ lines.

Two-Bit Synchronous Binary Up/Down Counter

• Uses T or J-K FFs.
• Up count: 00 → 01 → 10 → 11
• Down count: 11 → 10 → 01 → 00
• Direction control via input line.

Boolean Expression Simplification Using K-Map

• Same as Q7.
• Group 1s into rectangles (powers of 2).
• Simplify to minimize expression.

NAND and NOR as Universal Gates

• NOT A: A NAND A
• AND: (A NAND B)' = NAND followed by NOT
• OR: (A' NAND B')'

Binary Subtraction Using 2's Complement

• 2's complement of B: Invert + 1
• Add to A.
• Ignore carry if present.

Function Implementation Using NAND/NOR Gates

• Convert Boolean equation to SOP/POS.
• Apply DeMorgan's Theorem.
• Use only NAND or only NOR equivalents.

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