Lect9 Combinational Circuits

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    TA C162

    Lecture 9 Combinational Circuits

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    Todays AgendaDemorgans Law

    Adder

    Full Adder

    Saturday, January 30, 2010 2Biju K Raveendran@BITS Pilani.

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    Demorgans Law Suppose we complement an input before

    .

    For example, consider

    Observe, if inputs are 0 and 1

    then out ut is 1.

    Saturday, January 30, 2010 3Biju K Raveendran@BITS Pilani.

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    Demorgans Law -Converting AND to OR

    Exercise:

    A B A B A.B (A.B)

    0 1 1 0 0 1

    1 1 0 0 0 1

    Saturday, January 30, 2010 4Biju K Raveendran@BITS Pilani.

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    Demorgans Law

    (A.B) = A+B

    (A+B) = A.B

    . represents Logic AND

    + represents Logic OR represents Logic NOT

    Saturday, January 30, 2010 5Biju K Raveendran@BITS Pilani.

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    DeMorgan's LawFirst Law

    . . . . . = = + + + + .

    Second Law

    A+B+C+D . = = A.B.C.D. .

    Here . represents Logic AND

    +

    Saturday, January 30, 2010 6Biju K Raveendran@BITS Pilani.

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    Logic Structures 2 kinds Storage Structures

    Permits the storage of information (as bits)

    ec s on ruc ures

    Does not include storage of information

    Outputs strictly depend on the combination of thecurrent in ut values

    Outputs are not dependent on the past historystored internally (no information can be storedn erna y n a com na ona ogc c rcu

    Saturday, January 30, 2010 7Biju K Raveendran@BITS Pilani.

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    Combinational Logic Structures

    Full Adder

    Multiplexer (MUX)

    Saturday, January 30, 2010 8Biju K Raveendran@BITS Pilani.

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    Lets Design a Circuit for Binary Addition

    Requirement

    Adds the 2 bits given and produces sum and carry

    (Half) ADDER

    0 0 1 1

    0 1 0 1

    sum

    carr

    Before proceeding to attempt drawing circuit Understand the input/output of the circuit

    Define the behavior of the circuit using truth table

    Write the Sum of Products SOP Boolean ex ressions from the

    truth table We dont bother the simplification process involved in reducing

    the circuitry complexity for now.

    Saturday, January 30, 2010 9Biju K Raveendran@BITS Pilani.

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    Adding two bits: Half AdderTruth Table:A B Sum Carry

    0 0 0 00 1 1 0

    1 0 1 0

    Boolean Expressions

    C = A AND B

    10

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    Adding Three Bits: Full Adder4-Bit Full Adder

    Requirement: Adds the two bits and a carry

    Saturday, January 30, 2010 11Biju K Raveendran@BITS Pilani.

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    Full Adder Performs the addition in column i

    3 inputs: ai, bi and ci

    ai i c i+1 s i0 0 0 0

    2 outputs: si and ci+1 ci is the carry in from bit position i-1

    1 0 0 11 1 1 0

    ci+1 is the carry out to bit position i+1

    a a ... a a

    n 1 n 2 1 0b b ... b b +

    n 1 n 2 1c c ... c +

    n n ...

    Saturday, January 30, 2010 12Biju K Raveendran@BITS Pilani.

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    Full Adder: Truth TableA B Cin S Cout0 0 0 0 0

    0 1 0 1 0

    1 0 0 1 0

    1 1 0 0 1

    SOP for Sum S = A.B.C + A.B.C + A.B.C + A.B.C

    = . . . . . . . .

    Saturday, January 30, 2010 13Biju K Raveendran@BITS Pilani.

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    Full Adder Logic Implementation

    Saturday, January 30, 2010 14Biju K Raveendran@BITS Pilani.