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2 Combinational Logic Circuit 01
 

2 Combinational Logic Circuit 01

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    2 Combinational Logic Circuit 01 2 Combinational Logic Circuit 01 Presentation Transcript

    • 논리회로 설계실험
      담당교수 : 전재욱
      담당조교 : 석민식, 송지호
    • 2
    • 1 Analog & digital
      Sub. Contents.
      1.1 Analog & Digital
      1.2 Analog
      1.3 Digital
      3
    • 1.1 Analog & Digital
      4
      Analog
      Digital
      V
      V
      T
      T
      0
      0
    • 1.2 Analog
      5
      Input Signal
      Output Signal
      양적인 비례 관계
    • 1.3 Digital
      6
      Input Signal
      Output Signal
      논리적인 비례 관계
    • 2 Binary digit operation
      Sub. Contents.
      2.1 Binary System
      2.2 Boolean Algebra
      2.3 Venn Diagram
      7
    • 2.1 Binary System
      • Binary System
      0과 1로 이루어진 수
      표기법 : 10001001(2)
      • Decimal to Binary Conversion
      8
      2
      65
      32 … 1
      2
      16 … 0
      2
      128 64 32 16 8 4 2 1
      1000001
      2
      08 … 0
      0 1 0 0 0 0 0 1
      Binary :
      2
      04 … 0
      2
      02 … 0
      01 … 0
    • 2.2 Boolean Algebra
      Logical Sum : +
      ► A + B = Y
      0 + 0 = 0
      0 + 1 = 1
      1 + 1 = 1
      Logical Product : •
      ► A • B = Y
      0 • 0 = 0
      0 • 1 = 0
      1 • 1 = 1
      Logical Not : /, ‾,n,`
      ► A ( /A, nA, A`) = Y
      0 = 1
      1 = 0
      9
      Truth Table
    • 2.2 Boolean Algebra – Single Variable
      AND
      X • 0 = 0
      X • 1 = X
      X • 0 = 0
      X • X = 0
      NOT
      X = X
      OR
      X + 0 = X
      X + 1 = 1
      X + X = X
      X + X = 1
      10
    • 2.2 Boolean Algebra – Multi Variable
      • Commutative Law
      X + Y = Y + X
      X • Y = Y • X
      • Associative Law 
      X + (Y + Z) = (X + Y) + Z = X + Y + Z
      X(Y • Z) = X • Y • Z = XYZ
      • Distributive Law
      X(Y+Z) = X • Y + X • Z = XY + XZ
      (X + W)(Y + Z) = X • Y + X • Z + W • Y + W • Z = XY + XZ + WY + WZ
      • Other Law
      X + XY = X
      X + XY = X + Y
      11
    • 2.3 Venn Diagram
      12
      XY
      XY
      XY
    • 2.4 De-Morgan Law
      13
      A + B = A • B
      A • B = A + B
    • 3 Gate symbol
      Sub. Contents.
      3.1 Buffer & NOT Gate
      3.2 AND & NAND Gate
      3.3 OR & NOR Gate
      3.4 XOR & ExOR Gate
      3.5 Relativity Theorem
      14
    • 3.1 Buffer & NOT Gate
      15
      NOT Gate
      Buffer
      Input
      Output
      Input
      Output
    • 3.1 Buffer & NOT Gate - Analog Not Gate Circuit
      16
      B = 0
      C
      Output
      Input
      B
      E
      B = 1
    • 3.2 AND & NAND Gate
      17
      AND Gate
      NAND Gate
      Input A
      Input A
      Output
      Output
      Input B
      Input B
    • 3.2 AND & NAND Gate - Analog AND Gate Circuit
      18
      B
      C
      =>
      C
      E
      B
      E
      < TR >
      < Switch >
      Input A
      Input B
      Output
    • 3.3 OR & NOR Gate
      19
      OR Gate
      NOR Gate
      Input A
      Input A
      Output
      Output
      Input B
      Input B
    • 3.3 OR & NOR Gate - Analog OR Gate Circuit
      20
      Input A
      Input B
      Output
    • 3.4 XOR & ExOR Gate
      21
      ExOR(XOR) Gate
      ExNORGate
      Input A
      Input A
      Output
      Output
      Input B
      Input B
      A ⊙ B = Y
      A B = Y
    • 3.5 Relativity Theorem
      A + B = B + A
      A+(B+C) = (A+B)+C
      A(B+C) = A•B+A•C
      A+0=A
      A+1=1
      A+A=A
      A+A=1
      A=A
      A+B=A•B
      A+A•B=A
      A+A•B=A+B
      A•B=B•A
      A(B•C)=(A•B)C
      A+B•C=(A+B)(A+C)
      A•1=A
      A•0=0
      A•A=A
      A•A=0
      A=A
      A•B=A+B
      A(A+B)=A
      A(A+B)=A•B
      22
    • 4 Combinational Logic Circuit
      Sub. Contents.
      4.1 Combinational Logic
      4.2 Half-Adder
      4.3 Full-Adder
      4.4 Half-Subtracter
      4.5 Full-Subtracter
      4.6 Subtraction
      4.7 Adder-Subtracter
      23
    • 4.1 Combinational Logic
      24
      Input A
      Input B
      Output
      Input C
      Input D
      (A+B) (CD) = Output
    • 4.2 Half-Adder
      25
      Input A
      SUM
      Input B
      CARRY
      (A B) = SUM
      A • B = CARRY
    • 4.2 Half-Adder
      26
      0
      +0
      00
      1
      +0
      01
      0
      +1
      01
      1
      +1
      11
      Half
      Adder
      Input A
      SUM
      Input B
      CARRY
      Half
      Adder
      Half
      Adder
      Half
      Adder
      Half
      Adder
      Half
      Adder
      Half
      Adder
      Half
      Adder
      0010011
      +1000001
      1010010
      CARRY ?
    • 4.3 Full-Adder
      27
      SUM
      Input A
      Half
      Adder
      Half
      Adder
      Input B
      CARRY
      Input C
    • 4.3 Full-Adder
      28
      Input A
      SUM
      Input B
      Carry
      Carry
      Input
    • 4.3 Full-Adder
      29
      A1
      A2
      A3
      A4
      A5
      A6
      A7
      A8
      B1
      B2
      B3
      B4
      B5
      B6
      B7
      B8
      SUM1
      SUM2
      SUM3
      SUM4
      SUM5
      SUM6
      SUM7
      SUM8
      CARRY
      Full
      Adder
      Full
      Adder
      Full
      Adder
      Full
      Adder
      Full
      Adder
      Full
      Adder
      Full
      Adder
      Half
      Adder
      10010011
      +10010001
      100100100
    • 4.4 Half-Subtracter
      30
      Input A
      Data
      Half
      Subtracter
      (HS)
      Input B
      1
      -1
      00
      1
      -0
      01
      0
      -1
      11
      0
      -0
      00
      Borrow
      Input A
      SUM
      Input B
      Borrow
    • 4.5 Full-Subtracter
      31
      Data
      Input A
      HS
      HS
      Input B
      Borrow
      Input C
    • 4.5 Full-Subtracter
      32
      Input A
      Data
      Input B
      Borrow
      Borrow
      Input
    • 4.5 Full-Subtracter
      33
      A1
      A2
      A3
      A4
      A5
      A6
      A7
      A8
      B1
      B2
      B3
      B4
      B5
      B6
      B7
      B8
      D1
      D2
      D3
      D4
      D5
      D6
      D7
      D8
      Borrow
      FS
      FS
      FS
      FS
      FS
      FS
      FS
      HS
      10011001
      -01000001
      101011000
    • 4.6 Subtraction
      34
      10011001
      -01000001
      ?
      One’s complement
      Two’s complement
      10111111
      10111110
      10011001
      +10111111
      101011000
      10011001 = 153
      01000001 = 65
      153 - 65 = 88
      88
    • 4.7 Adder-Subtracter
      35
      A1
      A2
      A3
      A4
      A5
      A6
      A7
      A8
      B1
      B2
      B3
      B4
      B5
      B6
      B7
      B8
      Sel
      FA
      FA
      FA
      FA
      FA
      FA
      FA
      FA
      D1
      D2
      D3
      D4
      D5
      D6
      D7
      D8
      10011001
      +10111111
      001011000
      10011001
      -01000001
      ?
      Plus & Minus Code
    • 36
      End of Page