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    Tugas 2

    Uploaded by

    Muhammad Fahmi
    The document contains examples of proving the identities of Boolean algebra expressions through algebraic manipulation. It includes identities to prove for expressions with variables such as A, B, C, D, X, Y, Z. It also contains examples of simplifying Boolean expressions to a specified number of literals. Finally, it discusses finding the complements of Boolean expressions using De Morgan's theorems and properties of complements.

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    Tugas 2

    Uploaded by

    Muhammad Fahmi
    909 views5 pages
    The document contains examples of proving the identities of Boolean algebra expressions through algebraic manipulation. It includes identities to prove for expressions with variables such as A, B, C, D, X, Y, Z. It also contains examples of simplifying Boolean expressions to a specified number of literals. Finally, it discusses finding the complements of Boolean expressions using De Morgan's theorems and properties of complements.

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    TUGAS 2

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    The document contains examples of proving the identities of Boolean algebra expressions through algebraic manipulation. It includes identities to prove for expressions with variables such as A, B, C, D, X, Y, Z. It also contains examples of simplifying Boolean expressions to a specified number of literals. Finally, it discusses finding the complements of Boolean expressions using De Morgan's theorems and properties of complements.

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    909 views5 pages

    Tugas 2

    Uploaded by

    Muhammad Fahmi
    The document contains examples of proving the identities of Boolean algebra expressions through algebraic manipulation. It includes identities to prove for expressions with variables such as A, B, C, D, X, Y, Z. It also contains examples of simplifying Boolean expressions to a specified number of literals. Finally, it discusses finding the complements of Boolean expressions using De Morgan's theorems and properties of complements.

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    Tugas Pengantar Sistem Digital Bab 2

    2.2 Prove the identity of each the following Boolean equations, using algebric manipulation. a. + Y + XY + Y + X Y + Y X +

    = Y+ = X Y + = b. +Y B+

    +AB+

    C + C

    = B + A B + = B A + =B + B =1

    + C +

    c. Y + XZ + XY X + Y + Z = Y + XY + XZ = Y + XY + Y+ XZ = Y + X + XZ = Y + X + XX + Z =X+Y+Z d. XY YZ XZ XY YZ XY XZ YZ
    XY YZ XZ XY ( Z Z ) YZ XY XZ YZ XY YZ XZ XYZ XYZ YZ XY XZ YZ XY YZ XZ (1 Y ) YZ (1 X ) XY XZ YZ XY YZ XZ YZ XY XZ YZ XY YZ ( X X ) XZ YZ XY XZ YZ XY XYZ XYZ XZ YZ XY XZ YZ XY (1 Z ) XZ (1 Y ) YZ XY XZ YZ XY XZ YZ XY XZ YZ

    2.3 Provide the identity of each of following Boolean equaition, using algebraic manipulation.
    a)

    ABC BCD BC CD B CD

    C ( AB BD D) BC B CD C ( AB B D) BC B CD ABC BC CD BC B CD ABC CD B(C C ) B CD ABC CD B B CD B( AC 1) CD B CD B CD B CD


    b) WY WYZ WXZ WXY WY WXZ XYZ XYZ

    (WY WXYZ ) (WXYZ WXYZ ) (WXYZ WXYZ ) (WXYZ WXYZ ) WY WXZ XYZ XYZ (WY WXYZ ) (WXYZ WXYZ ) (WXYZ WXYZ ) (WXYZ WXYZ ) WY WXZ XYZ XYZ WY (1 YZ ) WXZ (Y Y ) XYZ (W W ) XYZ (W W ) WY WXZ XYZ XYZ WY .1 WXZ .1 XYZ .1 XYZ .1 WY WXZ XYZ XYZ WY WXZ XYZ XYZ WY WXZ XYZ XYZ

    c)

    AD AB CD BC ( A B C D)( A B C D)

    AD AB CD BC ( A B C D)( A B C D ) AD. AB.CD.BC ( A B C D)( A B C D ) ( A D)( A B )(C D )( B C ) ( A B C D )( A B C D ) ( AA AB AD BD)( BC CC BD DC ) ( A B C D )( A B C D ) ( AB AD BD)( BC BD DC ) ( A B C D )( A B C D ) ABCD ABCD ( A B C D)( A B C D) ( A B C D)( A B C D) ( A B C D)( A B C D )
    2.4 A.B = 0 dan A+B= 1, buktikan (A + C) ( + (A + C) ( + ( ( ( ( ( ( ( (

    2.6 simplify the following Boolean expression to the indicated number of literials: a. (

    ( ( ( b. ( = = = c. A B

    +( + +

    + ) +

    +AC

    = A ( C+ B ) = A ( (C+ B)+ (C+ )) = A (C + B) d. =D( = D (( = D ( +B =D( =D( =D ( +B) e. ( =A =A . A C. ( C( ( ( +B+ ) ( ( ) ) ) D+ D+BD ) )

    +B+ )

    = 0+0+0 =0

    2.7 Reduce the following Boolean expression to the indicated number of literials: a. ( ( b. X + Y ( Z + =X+Y(Z+XZ) =X+Y(Z+X)(Z+Z) =X+YZ+XY = ( X + X )( X + Y ) + Y Z =X+Y+YZ =X+Y c. W X ( Z + Y Z ) + X (W + W Y Z ) =WXZ+WXYZ+WX+WXYZ =WXZ+WXZ+WX =WX+WX =X d. (AB + AB)(CD + CD) + AC = ABCD + ABCD + ABCD + ABCD + A + C = ABCD + A + C = A + C + A(BCD) = A + C + C(BD) = A + C + BD ) ( ( ( (1)

    2.8 Using De Morgans theorem, express the function F=

    a. With only OR and complement operations.

    b. With only AND and complement operations. a.

    (A+B+C) + (A + C) + (A + B)

    b.

    F = ABC + AC + AB = (ABC).(AC).(AB)

    2.9 Find the complement of the following expression : a. F = (A + B)(A + B) b. F = ((V + W)X + Y)Z c. F = [W + X + (Y + Z)(Y + Z)][W + X + YZ + YZ] d. F = ABC + (A + B)C + A(B + C)

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