Boolean Logic
- 2. Representing Boolean Values Domain Values Mathematics True False Computer Science 1 0 Electronics On Off Vcc Ground
- 3. Boolean Logic Notation Mathematical Formal Typed A’B’CD + AB’CD Java/C !A&&!B&&C&&D||A&&!B&&C&&D ¬A ¬ᴧ BᴧCᴧD ᴠA ¬ᴧ BᴧCᴧD A.B.C.D + A.B.C.D
- 4. Truth Tables A B C D X 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0
- 5. Truth Tables A B C D X 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0
- 6. Binary Boolean Logic Operators A B 0 NOR NOTA B XOR NAND AND XNOR NOTB A OR 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 NOT(B→A) NOT(A→B) A→B B→A
- 7. Boolean Implication A B 0 NOR NOTA B XOR NAND AND XNOR NOTB A OR 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 NOT(B→A) NOT(A→B) A→B B→A
- 8. Sum of Products ANDANDANDANDAND OR BADCB DCBAD ACAA DC ABCD + ABD + ABCD + AC + ACD
- 9. Minterm Form A B C D X Y 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 X = ABCD + ABCD + ABCD + ABCD Y = ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD
- 10. Reduction X = ABCD + ABC + ABCD X = ABCD + ABC(D + D) + ABCD X = ABCD + ABCD + ABCD + ABCD X = ABCD + ABC.1 + ABCD
- 12. Conclusion