ECE 462 Logic Design
Homework 6
1) Divide F = ab + ac + ad’ + bc + bd’ by G = a + b to give a G + RQ form
answer [5 points]
2) Apply the WEAK_DIV procedure to F = abrs + abrt + abd + abe + abu
+ ghrs + ghrw + ghd + ghe + ghu + dp + eq + rstuw and divisor
D = ab + gh.
Obtain Q = F/D and R [8 points]
3) How would you traverse the factoring tree representing a given factored
form, for getting maximal factors?
Show with 2 examples why your answer is correct [8 points]
4) Compute the factorization value for each of the following pairs of SOP
and factored form.
ab+ac+ad+b’c+b’d ab+(c+d)(a+b’)
ad+ae+bcd (a+bc)(d+ae)
Use Lits (P) = No: of literals in SOP form
[5 points]
5) Are the following pairs of factored forms equivalent? Are they
syntactically equivalent?
a(b’+c’)+a’(b+c)+a’c+b’c (a+b+c)(a’+b’+c’)
w(xy+z)+x’y’ x’y’+w(z+xy)
[6 points]
6) During resubstitution, as we studied in class, a few filters are applied to
circumvent useless divisions. Fj is not an algebraic divisor of Fi if:
1. j is not a fanout of a fanin of i
2. Fj contains a literal not in Fi
3. Fj has more terms than Fi
4. For any literal, the number of times it occurs in Fj exceeds that in Fi.
5. Fi is in the transitive fanin of Fj
