FIT1047 week 3

Which of these expressions is in sum-of-products (SOP) form? (note: X' means not X)

• XY + XYZ' + X'Y'Z'

• XY(Y' + Z) + Z'

• (Z' + X)(Z + Y')

• (XY)'+Y'(XZ)'

To convert a truth table to sum-of-products (SOP) form, we:

• sum the products for every row that has a FALSE output

• sum the products for every row that has a TRUE output

• sum the products for every row that has a FALSE or TRUE output

What is the correct sum-of-products representation for this truth table?

• X'Y'Z' + XY + XY'Z' + XYZ

• X'YZ' + XY'Z' + XY'Z + XYZ

• Z + YZ + XYZ

• X'Y'Z' + X'Y'Z + X'YZ + XYZ'

Which of these is a correct Karnaugh map for this truth table?

• 
• 
• 

Which of these are the correct groups for the Karnaugh map?

• 
• 
• 

Which of these is the correct sum-of-products expression corresponding to these Karnaugh map groups?

• X'Y' + X'Z + XYZ'

• X'Z' + XY + XYZ'

• XY + X'Z + XYZ'

• X'Y'Z' + X'Y'Z + X'YZ + XYZ'

Applying De Morgan's law to (XY'Z + X'Y'Z + XYZ)' gives:

• (X'YZ')(XYZ')(X'Y'Z')

• (XY'Z)'(X'Y'Z)'(XYZ)'

• (X'YZ')'(XYZ')'(X'Y'Z')'

• (XY'Z)(X'Y'Z)(XYZ)

Applying De Morgan's law to (XY'Z)'(X'Y'Z)'(XYZ)' gives

• (X + Y' + Z)'(X' + Y' + Z)'(X + Y + Z)'

• (X' + Y + Z')(X + Y + Z')(X' + Y' + Z')

• (X'YZ')(XYZ')(X'Y'Z')

• (X + Y' + Z)(X' + Y' + Z)(X + Y + Z)