The truth table for the output Y in terms of three inputs A, B and C are given in table. Draw a logic circuit realization using only NOR gates.

Signals A,B,C,D and $$\overline D $$ are available. Using a single 8 - to - 1 multiplexer and no other gate, implement the Boolean function.

$$f(A,B,C,D) = B.C + A.B.\bar D + \bar A.\bar C.\bar D$$

A pulse train with a frequency of 1 MHz is counted using a modulo-1024 ripple-counter built with J-K flip flops. For proper operation of the counter, the maximum permissible propagation delay per flip flop stage is ______ n sec.

2’s complement representation of a 16-bit number (one sign bit and 15 magnitude bits) is FFFI. Its magnitude in decimal representation is