A function of Boolean variables X,Y and Z is expressed in terms of the min-terms as F(X, Y, Z)=$$\sum\limits_{}^{} {} $$m(1,2,5,6,7) Which one of the product of sums given below is equal to the funtion F(X, Y, Z)?

In the figure shown, the output ܻ is required to be ܻ Y=AB+ $$\overline C $$$$\overline D $$. The gates G1 and G2 must be, respectively,

A 1-to-8 demultiplexer with data input D$$_{in}$$ , address inputs S$$_{0}$$, S$$_{1}$$, S$$_{2}$$ (with S$$_{0}$$ as the LSB) and $${\overline Y _0}$$ to $${\overline Y _7}$$ as the eight demultiplexed outputs, is to be designed using two 2-to-4 decoders (with enable input $$\overline E $$ and address inputs A$$_{0}$$ and A$$_{1}$$) as shown in the figure. $${D_{in}}$$, S$$_{0}$$, S$$_{1}$$and S$$_{2}$$ are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R, and S terminals should be

A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in the figure. The value of n is _______.