problem 1:

a) Simplify the following Boolean function using 5 variable maps:

F = A’B’CE’+ A’B’C’D’ + B’D’E’ + B’CD’ + CDE’ + BDE’
 
b) Simplify the function F together with the don’t – care conditions in POS:

F(a,b,c,d) = ∑ (3,4,13,15)+ d (a,b,c,d) = ∑ (1,2,5,6,8,10,12,14)
 
c) Implement the following function with NAND gages f (x,y,z) = ∑ (0,6)

problem 2:

a) Implement the following function with NOR gates f (x,y,z) = ∑ (0,6)

b) Simplify the following functions in POS F (a,b,c,d) = II (1,3,5,7,13,15)
 
c) Simplify the function F together with the don’t – care conditions in SOP

F(w,x,y,z) = ∑ (0,1,2,3,7,8,10) d (w,x,y,z) = (5,6,11,15)
 
problem 3:

a) Simplify the following Boolean functions using 4 variable map

ab’c + b’c’d + bcd + acd’ + a’b’c + a’bc’d
 
b) Simplify the following Boolean function F together with the don’t care conditions d; then express the simplified function in sum of mintems

F(w,x,yz) = ∑ (0,6,8,13,14) d (w,x,y,z) = ∑ (2,4,10)
 
c) Find the minterms of the following Bollean expression by first plotting each function in a map:

i) xy+yz+xy’z

ii) c’d+abc’+abd’+a’b’d
 
problem 4:

a) Simplify the given Boolean functions using 3 variable Kmap:

i) F (x,y,z) = ∑ (0,1,5,7)

ii) F (x,y,z) = ∑ (1,2,3,6,7)
 
b) Simplify the following Boolean functions using 3 variable map:

i) xy+x’y’z’+x’yz’

ii) x’y’+yz+x’yz’

c) Simplify the following Boolean functions using 4 variable K map:

i) w’z’ + xz + x’z + wx’z

ii) b’d + a’bc’+ab’c+abc’