Second Semester_Digital Logic_Basic Logic Gates

🔹 Basic Logic Gates

1. NOT Gate (Inverter)

• Equation: $Y = \overline{A}$

• Truth Table:

  • $A=0 \Rightarrow Y=1$

  • $A=1 \Rightarrow Y=0$

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2. AND Gate

• Equation: $Y = A \cdot B$ (sometimes written as $AB$)

• Truth Table:

  • $0 \cdot 0 = 0$

  • $0 \cdot 1 = 0$

  • $1 \cdot 0 = 0$

  • $1 \cdot 1 = 1$

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3. OR Gate

• Equation: $Y = A + B$

• Truth Table:

  • $0+0 = 0$

  • $0+1 = 1$

  • $1+0 = 1$

  • $1+1 = 1$

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🔹 Universal Gates

4. NAND Gate (NOT-AND)

• Equation: $Y = \overline{A \cdot B}$

• Truth Table:

  • $0 \cdot 0 = 0 \Rightarrow 1$

  • $0 \cdot 1 = 0 \Rightarrow 1$

  • $1 \cdot 0 = 0 \Rightarrow 1$

  • $1 \cdot 1 = 1 \Rightarrow 0$

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5. NOR Gate (NOT-OR)

• Equation: $Y = \overline{A + B}$

• Truth Table:

  • $0+0 = 0 \Rightarrow 1$

  • $0+1 = 1 \Rightarrow 0$

  • $1+0 = 1 \Rightarrow 0$

  • $1+1 = 1 \Rightarrow 0$

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🔹 Exclusive Gates

6. XOR (Exclusive-OR)

• Equation: $Y = A \oplus B = A\overline{B} + \overline{A}B$

• Truth Table:

  • $0 \oplus 0 = 0$

  • $0 \oplus 1 = 1$

  • $1 \oplus 0 = 1$

  • $1 \oplus 1 = 0$

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7. XNOR (Exclusive-NOR / Equivalence)

• Equation: $Y = \overline{A \oplus B} = AB + \overline{A}\,\overline{B}$

• Truth Table:

  • $0 \text{ XNOR } 0 = 1$

  • $0 \text{ XNOR } 1 = 0$

  • $1 \text{ XNOR } 0 = 0$

  • $1 \text{ XNOR } 1 = 1$

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✅ Summary Table (Equations Only)

Gate	Symbol	Equation
NOT	$\overline{A}$	Inverts input
AND	$A \cdot B$	Outputs 1 if both are 1
OR	$A + B$	Outputs 1 if any is 1
NAND	$\overline{A \cdot B}$	Inverse of AND
NOR	$\overline{A + B}$	Inverse of OR
XOR	$A \oplus B = A\overline{B} + \overline{A}B$	Outputs 1 if inputs differ
XNOR	$\overline{A \oplus B} = AB + \overline{A}\,\overline{B}$	Outputs 1 if inputs are same