CSC 370 - Computer Architecture and Organization

Dr. R. M. Siegfried

Assignment 3 - p.118-120/3-1, 3-3, 3-5, 3-15

Due Wednesday, September 20, 2023

3-1.

Simplify the following Boolean functions using three-variable maps:

  1. F(x, y, z) = Σ(0, 2, 4, 5)
  2. F(x, y, z) = Σ(0, 2, 4, 5, 6)
  3. F(x, y, c) = Σ(0, 1, 2, 3, 5)
  4. F(x, y, z) = Σ(1, 2, 3, 7)

3-3.

Simplify the following Boolean expressions using three-variable maps:

  1. F(x, y, z) = xy + x'y'z' + x'yz'
  2. F(x, y, z) = x'y' + yz + x'yz'
  3. F(x, y, z) = x'y + yz' + y'z'
  4. F(x, y, z) = x'yz + xy'z' + xy'z

3-5.

Simplify the following Boolean functions using four-variable mps:

  1. F(w, x, y, z) = Σ(1, 4, 5, 6, 12, 14, 15)
  2. F(A, B, C, D) = Σ(2, 3, 6, 7, 12, 13, 14)
  3. F(w, x, y, z) = Σ(1, 3, 4, 5, 6, 7, 9, 11, 13, 15)
  4. F(A, B, C, D) = Σ(0, 2, 4, 5, 6, 7, 8, 10, 13, 15)

3-15

Simplify the following Boolean function F, together with the don't-care conditions d and then express the simplified function in terms of minterms:

  1. F(x, y, z) = Σ(0, 1, 4, 5, 6)
    d(x, y, z) = Σ(2, 3, 7)
  2. F(A, B, C, D) = Σ(0, 6, 8, 13, 14)
    d(A, B, C, D) = Σ(2, 4, 10)
  3. F(A, B, C, D) = Σ(5, 6, 7, 12, 14, 15)
    d(A, B, C, D) = Σ(3, 9, 11, 15)
  4. F(A, B, C, D) = Σ(2, 4, 7, 10, 12)
    d(A, B, C, D) = Σ(0, 6, 8)

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