Positive&Negative Logic

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  • 8/10/2019 Positive&Negative Logic

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    Logic Gates

    The Logic gates are electronic circuits that can be used to implement the most

    elementary logic expressions, also known as Boolean expressions. The logic gate is

    the most basic building block of combinational logic. There are three basic logic

    gates, namely the OR gate, the A! gate and the OT gate. Other logic gates that

    are deri"ed from these basic gates are the A! gate, the OR gate, the

    #$%L&'()#OR gate and the #$%L&'()#*OR gate.

    Positive and Negative Logic

    The binary "ariables, as we know, can ha"e either of the two states, i.e. the logic +-

    state or the logic +- state. These logic states in digital systems such as computers, for

    instance, are represented by two different "oltage le"els or two different current

    le"els. (f the more positi"e of the two "oltage or current le"els represents a logic +-

    and the less positi"e of the two le"els represents a logic +-, then the logic system is

    referred to as a positive logic system. (f the more positi"e of the two "oltage or

    current le"els represents a logic +- and the less positi"e of the two le"els represents a

    logic +-, then the logic system is referred to as a negative logic system. The

    following examples further illustrate this concept. (f the two "oltage le"els are )

    and /0 ), then in the positi"e logic system the ) represents a logic +- and the /0 )

    represents a logic +-. (n the negati"e logic system, ) represents a logic +- and /0

    ) represents a logic +-. (f the two "oltage le"els are ) and 10 ), then in the

    positi"e logic system the ) represents a logic +- and the 10 ) represents a logic

    +-. (n the negati"e logic system, ) represents a logic +- and 10 ) represents a

    logic +-. (t is interesting to note, as we will disco"er in the latter part of the chapter,

    that a positi"e OR is a negati"e A!. That is, OR gate hardware in the positi"e logic

    system beha"es like an A! gate in the negati"e logic system. The re"erse is also

    true. 'imilarly, a positi"e OR is a negati"e A!, and "ice "ersa.

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    OR Gate

    An OR gate performs an ORing operation on two or more than two logic "ariables.

    The OR operation on two independent logic "ariables A and B is written as 2 3 A/B

    and reads as 2 e4uals A OR B and not as A plus B. An OR gate is a logic circuit with

    two or more inputs and one output. The output of an OR gate is LO5 only when all

    of its inputs are LO5. 6or all other possible input combinations, the output is 7(87.

    This statement when interpreted for a positi"e logic system means the following.

    The output of an OR gate is a logic +- only when all of its inputs are at logic +-. 6or

    all other possible input combinations, the output is a logic +-. 6igure below shows

    the circuit symbol and the truth table of a two*input OR gate. The operation of a two*

    input OR gate is explained by the logic expression9

    2 3 A/B

    A B 2

    As an illustration, if we ha"e four logic "ariables and we want to know the logical

    output of :A/ B/% /!;, then it would be the output of a four*input OR gate with A,

    B, % and ! as its inputs. 23A/B 6igures :a; and :b; show the circuit symbol of

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    three*input and four*input OR gates. 6igure :c; shows the truth table of a three*input

    OR gate. Logic expressions explaining the functioning of threei nput and four*input

    OR gates are 2 3 A/B/% and 2 3 A/B/% /!.

    Q/Ho ould you hardare!implement a "our!input O# gate using to!input O#

    gates only$

    =

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    Example : Draw the output waveform for the OR gate and the given pulsed input

    waveforms of Fig

    !ND Gate

    An A! gate is a logic circuit ha"ing two or more inputs and one output. The output

    of an A! gate is 7(87 only when all of its inputs are in the 7(87 state. (n all other

    cases, the output is LO5. 5hen interpreted for a positi"e logic system, this means

    that the output of the A! gate is a logic +- only when all of its inputs are in logic

    +- state. (n all other cases, the output is logic +-. The logic symbol and truth table of

    a two*input A! gate are shown below The A! operation on two independent

    logic "ariables A and B is written as 2 3 A.B and reads as 2 e4uals A A! B and not

    as A multiplied by B. 7ere, A and B are input logic "ariables and 2 is the output. An

    A! gate performs an A!ing operation9

    >

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    0

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    ? for a two*input A! gate, 2 3 [email protected]

    ? for a three*input A! gate, 2 3 A.B.%@

    ? for a four*input A! gate, 2 3 A.B.%.!.

    (f we interpret the basic definition of OR and A! gates for a negati"e logic system,

    we ha"e an interesting obser"ation. 5e find that an OR gate in a positi"e logic

    system is an A! gate in a negati"e logic system. Also, a positi"e A! is a negati"e

    OR.

    Example :

    Sho the logic arrangement "or implementing a "our!input AN% gate using to!input

    AN% gates only.

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    NO" Gate

    A OT gate is a one*input, one*output logic circuit whose output is always the

    complement of the input. That is, a LO5 input produces a 7(87 output, and "ice

    "ersa. 5hen interpreted for a positi"e logic system, a logic +- at the input produces a

    logic +- at the output, and "ice "ersa. (t is also known as a +complementing circuit- or

    an +in"erting circuit-.

    The OT operation on a logic "ariable $ is denoted as or . That is, if $ is the

    input to a OT circuit, then its output 2 is gi"en by 2 3 or and reads as 2 e4uals

    OT $. Thus, if $ 3 , 2 3 and if $ 3 , 2 3 .

    # $For the logic circuit arrangements of Figs %a& and %'&( draw the output

    waveform

    E)*L+,-.E/OR Gate

    The #$%L&'()#*OR gate, commonly written as #$*OR gate, is a two*input, one*

    output gate. 6igures :a; and :b; respecti"ely show the logic symbol and truth table of

    a two*input #$*OR gate. As can be seen from the truth table, the output of an #$*OR

    gate is a logic +- when the inputs are unlike and a logic +- when the inputs are like.

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    Although #$*OR gates are a"ailable in integrated circuit form only as two*input

    gates, unlike other gates which are a"ailable in multiple inputs also, multiple*input

    #$*OR logic functions can be implemented using more than one two*input gates.

    The truth table of a multiple*input #$*OR function can be expressed as follows. The

    output of a multiple*input #$*OR logic function is a logic +- when the number of s

    in the input se4uence is odd and a logic +- when the number of s in the input

    se4uence is e"en, including Cero. That is, an all s input se4uence also produces a

    logic +- at the output. 6igure:c; shows the truth table of a four*input #$*OR

    function. The output of a two*input #$*OR gate is expressed by

    2 3 AB 3 B/A

    D

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    #: 0ow do 1ou implement three/input and four/input )/OR logic functions with

    the help of two/input E)/OR gates2#: 0ow can 1ou implement a NO" circuit using a two/input E)/OR gate2

    N!ND Gate

    A! stands for OT A!. An A! gate followed by a OT circuit makes it a

    A! gate E6ig. :a;F. 6igure :b; shows the circuit symbol of a two*input A!

    gate. The truth table of a A! gate is obtained from the truth table of an A! gate

    by complementing the output entries E6ig. :c;F. The output of a A! gate is a logic

    G

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    +- when all its inputs are a logic +-. 6or all other input combinations, the output is a

    logic +-. A! gate operation is logically expressed as

    2 3

    (n general, the Boolean expression for a A! gate with more than two inputs can

    be written as

    2 3

    NOR Gate

    OR stands for OT OR. An OR gate followed by a OT circuit makes it a OR

    gate E6ig. :a;F. The truth table of a OR gate is obtained from the truth table of an

    OR gate by complementing the output entries. The output of a OR gate is a logic +-

    when all its inputs are logic +-. 6or all other input combinations, the output is a logic

    +-. The output of a two*input OR gate is logically expressed as

    2 3

    (n general, the Boolean expression for a OR gate with more than two inputs can be

    written as

    2 3

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    E)*L+,-.E/NOR Gate

    #$%L&'()#*OR :commonly written as #$*OR; means OT of #$*OR, i.e. the

    logic gate that we get by complementing the output of an #$*OR gate. The truth

    table of an #$*OR gate is obtained from the truth table of an #$*OR gate by

    complementing the output entries. Logically, The output of a two*input #$*OR gate

    is a logic +- when the inputs are like and a logic +- when they are unlike. (n general,the output of a multiple*input #$*OR logic function is a logic +- when the number

    of s in the input se4uence is odd and a logic +- when the number of s in the input

    se4uence is e"en including Cero. That is, an all s input se4uence also produces a

    logic +- at the output.

    2 3 3 AB/

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    Lecture NO: ThreeLogic LectureM.Sc Adham Hadi

    03 :

    ,how the logic arrangements for implementing:

    %a& a four/input N!ND gate using two/input !ND gates and NO" gates4

    %'& a three/input N!ND gate using two/input N!ND gates4

    %c& a NO" circuit using a two/input N!ND gate4

    %d& a NO" circuit using a two/input NOR gate4

    %e& a NO" circuit using a two/input E)/NOR gate

    03:

    0ow do 1ou implement a three/input E)/NOR function using onl1 two/input E)/

    NOR gates2