Alexandria Higher Institute of Engineering & Technology (AIET)
All Departments
first. Year
CE 112
Fundamental of logic design
Sheet(3)
supervisor:
Dr.zeineb El_Gazayerly
1. Which form of Boolean equation is better suited for completing truth tables and timing
diagram SOP or POS?
2. Why the Demorgan’s theorem is important in the simplification of Boolean expression?
3. Which method of encircling eight adjacent cells in karnaugh map procedures is the simplest
equation; two cells groups or fourcells groups or one group of eight cells?
4. Use the bubble pushing technique to convert the gates in figure
5. Express the complement of the following functions in sum of minterms and product of
maxterms
a)F(A,B,C,D)= ∑ (0,2,6,11,13,14)
b)F(X,Y,Z)= ∏ (0,3,6,7)
Given F (a,b,c)=b+a’c
a)Express f as minterm expansion (use m notation)
b) Express f as maxterm expansion (use M notation)
c) Express f’as minterm expansion (use m notation)
d) Express f’ as maxterm expansion (use M notation)
6. Simplify the following Boolean function in sum-of-products:
a)F(X,Y,Z)= ∑ m(0,1,2,4,5)+ ∑ d(3,6,7)
b)F(A,B,C,D)= ∏M(0,2,8,10,11,14). ∏D (4, 6, 12, 13)
7. Simplify the following Boolean functions using Karnaugh map
F(X, Y, Z) = ∑ (0, 2, 6, 7)
F (A, B, C) =A’B+BC’+B’C’
F(A,B,C,D)= ∑ (0,2,4,5,6,7,8,10,13,15)
F(A,B,C,D)= ∏M(0,2,8,10,11,14). ∏D (4, 6, 12, 13)
F(A,B,C,D)= ∏ (1,3,5,7,13,15)
8. Simplify the following expression in (1) sum-of-products and (2) product-of-sums
a)F(w,x,y,z)= ∑ (2,3,12,13,14,15)
b)F(A,B,C,D)= ∏ (0,1,2,4,5,6,8,9,10,12)
c) F (A, B, C, D) =AC’+B’D+A’CD+ABCD
9.
A switching network has three inputs and two outputs. The output variables, a and b,
represent the first and second bits, respectively, of a binary number N.N equals the
number of inputs which are 0.For example, if x=1,y=0,z=1 then a=0,b=1.
(a)Find the minterm expansion for a and b
(b)Find the maxterm expansion for a and b
Express each answer in abbreviated notation and also write it out in terms of x,y,z.
10 . A switching network has four inputs as shown below. A and B represent the first and
second bits of binary number N1. C and D represent the first and second bits of binary number
N2. The output of the network is to be 1 only if the product N1*N2 is less than or equal to 2.
(a)Find the minterm expansion for F.
(b) Find the maxterm expansion for F.
Express your answer in both decimal notation and algebraic form.
11. A combinational logic circuit has four inputs (A, B, C, and D) and one output Z. The output
is 1 iff the input has three consecutive 0’s or three consecutive 1’s for example, if
A=1,B=0,C=0,and D=0,then Z=1, But if A=0, B=1, C=0, and D=0, then Z=0. Design the circuit using
one 4-input OR gate and four 3-input AND gates.