EECS 31/CSE 31/ICS 151 Homework 3 Questions

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Problem 1

Question

(Map representation) Generate the map representations for the following Boolean functions.

  1. F = w'x' + xy +wy' +wx
  2. F = x1'x0'+x1'y0+y1y0+x1'y1+x0'y1
  3. F = w'z' +wz+w'y+yz
  4. F = w'x'z'+w'xy+wxz+wx'y+w'yz'

Problem 2

Question

(Map method) Using the map method, determine the prime implicants of the following Boolean functions.

  1. F = x1'x0'+y1y0+x1'x0y1'y0+x1'x0y1y0'+x1x0'y1y0'
  2. F = w'x'+w'xy+wx'y'+wx
  3. F = w'y'z'+xy'z+wyz+x'yz'
  4. F = w'y+w'x'z+xyz'+wx'y'+wy'z'

Problem 3

Question

(Map method) Find all the minimal covers for the following Boolean functions.

  1. F = w'x'+w'xy+wx+wx'y'+xy
  2. F = yz+w'z'+wy'z
  3. F = x'y'z'+wy'z+xyz+w'yz'
  4. F = wy'z'+wx'y'+w'y+w'x'y'z+wxyz'

Problem 4

Question

(Gate-array mapping) Convert the function wx'y'+yw'z'+yxz+yxw into

  1. 2-input NAND gates
  2. 3-input NAND gates
  3. 4-input NAND gates

Problem 5

Question

(Technology mapping) Using the library defined by Tables 3.14, 3.15 and 3.16, perform technology mapping and minimize the delay for the following Boolean functions.

  1. F = y1'(y0'+x0+x1)+x1(x0+y0')
  2. F = w'(x'z'+xy) +w(xz+x'y')
  3. F = w'x'z+w'xy+wxz+wx'y'
  4. F = wx'y'+y(w'z'+x(z+w))

Problem 6

Question

(Technology mapping) Derive a minimum-delay implementation for the carry-look-ahead function c4 = g3+p3g2+p3p2g1+p3p2p1g0+p3p2p1p0c0 that use:

  1. The custom library defined by Table 3.14.
  2. The custom library defined by Tables 3.14 and 3.15.
  3. The custom library defined by Tables 3.14, 3.15, 3.16.