DIGITAL LOGIC SYSTEM

Boolean Operations

Key Points to Include:

• AND (⋅ / ∧): Output 1 only if all inputs are 1.
• OR (+ / ∨): Output 1 if any input is 1.
• NOT (¬ / '): Output is opposite of input.

Input A       Input B     AND (A⋅B)     OR (A+B)     NOT A (¬A)

0             1           0               0             1

0             0           0               1             1

1             1           0               1             0

1             1           1               1             0

Boolean Expressions & Truth Tables

Key Points:

• Boolean Expression: A statement that results in True (1) or False (0).
• Truth Table: Shows all possible input combinations and their outputs.

Example: Boolean Expression: F = x AND y OR NOT z

X     Y     Z     x∧y     ¬z     F = x∧y + ¬z

0     0     0         0         1         1

0     1     0         0         1         1

1     0     1         0         0         0

1     1     0         1         1         1

Boolean Laws & Simplification

Key Points

• Laws make expressions shorter and easier to implement in circuits
• Important Laws to Include:
  • Identity: A+0=A, A⋅1=A
  • Null: A+1=1, A⋅0=0
  • Idempotent: A+A=A, A⋅A=A
  • Inverse: A + ¬A = 1, A⋅¬A = 0
  • De Morgan's: (A⋅B)' = A'+B', (A+B)' = A'⋅B'

Example:

• Simplify A + B + A⋅C → A + B
• Simplify (A+B)(A+C) → A + BC

Visuals:

• Step-by-step color-coded simplification
• Use small icons for AND (⋅), OR (+), NOT (¬) in each step

Logic Gates & Circuits

Key Points

• AND, OR, NOT, NAND, NOR, XOR
• Each gate has symbol + function table
• Circuit Implementation: Boolean expression → logic gate diagram

Examples:

1. Boolean Expression: AB + C → Logic Circuit (AND + OR gates)
2. Boolean Expression: (A+B)⊕(C+D) → XOR + OR + AND gates