ECE 275: Digital Design I

  1. Critical Path:

    • G1 -> G3 -> G4 -> G6 Total Time: 1 + 1 + 1 +1 = 4ns
    • G2 -> G5 -> G6 Total Time: 3 + 1 + 3 = 7ns
    • Path 1: G1 -> G3 -> G4 -> G6 Total Time: 1 + 1 + 1 + 1 = 4ns
    • Path 2: G2 -> G5 -> G6 Total Time: 1 + 2 + 1 = 4ns
    • Path 3: G2 -> G5 -> G7 Total Time: 1 + 2 + 1 = 4ns
    • Path 4: G1 -> G5 -> G6 Total Time: 1 + 2 + 1 = 4ns
    • Path 5: G1 -> G5 -> G7 Total Time: 1 + 2 + 1 = 4ns
  2. Convert a. K-Map:

  3. AB\CD 00 01 11 10
    00 1
    01
    11 1 1
    10 1 1
    ~~SOP = m3 + m10 + m11 + m14 + m15~~
    SOP = AD(B + B')(D + D') + (A + A')(B'CD)
    **SOP = ABCD + ABC'D + AB'CD + AB'C'D + A'B'CD**
    b. K-Map:
    AB\CD 00 01 11 10
    00 0
    01
    11 0 0
    10 0 0 0
    ~~POS = M1 * M8 * M9 * M10 * M12 * M14~~
    POS = (B + C + D '+ A * A')(A' + D + C * C' + B * B')
    POS = (B + C + D' + A)(B + C + D' + A')(A' + D + CC' + B)(A' + D + CC' + B')
    **POS = (B + C + D' + A)(B + C + D' + A')(A' + D + C + B)(A' + D + C + B')(A' + D + C' + B)(A' + D + C' + B')**
    1. K-Map:
    AB\CD 00 01 11 10
    00 1 1 1 1
    01 1 1 0 1
    11 1 0 0 0
    10 1 1 0 0
    • F = m0 + m1 + m2 + m3 + m4 + m5 + m6 + m8 + m9 + m12
    • F = A'B' + C'D' + A'C' + B'C' + A'D'
    • F = M7 M10 M11 M13 M14 * M15
    • F = (A' + B' + D')(B' + C' + D')(A' + C')
    1. K-Map:
    AB\CD 00 01 11 10
    00 X 0 X 1
    01 1 X 1 X
    11 X 0 X 1
    10 0 X 1 X
    • F = ∑m(2, 4, 7, 11, 14) + ∑d(0, 3, 5, 6, 9, 10, 12, 15)
    • F = Ï€M(1, 8, 13) * Ï€D(0, 3, 5, 6, 9, 10, 12, 15)
    1. K-Map:
    AB\CD 00 01 11 10
    00 1 1 X
    01 X 1
    11 1 X X
    10 1 1
    • F = CD + BC + A'B'C' + AC'D'
    AB\CD 00 01 11 10
    00 0 0 X
    01 0 X
    11 X X X
    10 X 0
    • F = (B' + C + D)(C' + D')(A + B + D')
    A B C D F
    0 0 0 0 1
    0 0 0 1 0
    0 0 1 0 0
    0 0 1 1 0
    0 1 0 0 1
    0 1 0 1 1
    0 1 1 0 0
    0 1 1 1 0
    1 0 0 0 0
    1 0 0 1 0
    1 0 1 0 1
    1 0 1 1 1
    1 1 0 0 1
    1 1 0 1 1
    1 1 1 0 1
    1 1 1 1 1

    AB\CD 00 01 11 10
    00 1 1
    01 1 1 1
    11 1
    10 1 1

    Implicants: 1, 3, 4, 5, 7, 8, 9, 12 PI: 1, 3, 5, 7 EPI: 9 Implicants: 8 (# of implicants) PI: All the groups EPI: Groups with 1's only covered by said group

    AB\CD 00 01 11 10
    00 1 1 1
    01 1 1
    11 1 1
    10 1 1 1

    Implicants: 0, 2, 3, 5, 7, 8, 10, 11, 14, 15 PI: 10, 11, 14, 15 and 3, 7, 11, 15 and 0, 2, 8, 10 EPI: 5 SEE PART A

    F1
    X\YZ 00 01 11 10
    0 1 1
    1 1
    F2
    X\YZ 00 01 11 10
    0 1 1 1
    1
    F3
    X\YZ 00 01 11 10
    0 1 1
    1 1