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Simplify each boolean expression:

5. ABC ABC +ABC 6. ABC+ABC 7. ABC +AB(CD + EF)

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Answer #1

4) Here, A+B+\bar{A}\bar{B}

= A+(B+\bar{A})(B+\bar{B})

= A+(B+\bar{A})I

= A+B+\bar{A}

= (A+\bar{A})+B

= I+B

= I

5) \bar{A}BC+A\bar{B}C+ABC

= \bar{A}BC+ABC+A\bar{B}C

= (\bar{A}+A)BC+A\bar{B}C

= I.BC+A\bar{B}C

= BC+A\bar{B}C

= (B+A\bar{B})C

= [(B+A)(B+\bar{B})]C

= [(B+A).I]C

= (B+A)C

= BC+AC

6) \bar{A}\bar{B}\bar{C}+\bar{A}\bar{B}\bar{C}

= \bar{A}\bar{B}(\bar{C}+\bar{C})

= \bar{A}\bar{B}.\bar{C}

= \bar{A}\bar{B}\bar{C}

7) ABC+AB(CD+EF)

= ABC+ABCD+ABEF

= ABC.I+ABC.D+ABEF

= ABC.(I+D)+ABEF

= ABC.I+ABEF

= ABC+ABEF

= AB.C+AB.EF

= AB(C+EF)

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Answer #1

4) Here, A+B+\bar{A}\bar{B}

= A+(B+\bar{A})(B+\bar{B})

= A+(B+\bar{A})I

= A+B+\bar{A}

= (A+\bar{A})+B

= I+B

= I

5) \bar{A}BC+A\bar{B}C+ABC

= \bar{A}BC+ABC+A\bar{B}C

= (\bar{A}+A)BC+A\bar{B}C

= I.BC+A\bar{B}C

= BC+A\bar{B}C

= (B+A\bar{B})C

= [(B+A)(B+\bar{B})]C

= [(B+A).I]C

= (B+A)C

= BC+AC

6) \bar{A}\bar{B}\bar{C}+\bar{A}\bar{B}\bar{C}

= \bar{A}\bar{B}(\bar{C}+\bar{C})

= \bar{A}\bar{B}.\bar{C}

= \bar{A}\bar{B}\bar{C}

7) ABC+AB(CD+EF)

= ABC+ABCD+ABEF

= ABC.I+ABC.D+ABEF

= ABC.(I+D)+ABEF

= ABC.I+ABEF

= ABC+ABEF

= AB.C+AB.EF

= AB(C+EF)

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