problem 1)a) Name the different notations used for the representation of signed binary numbers. Suppose eight bits are available for the representation of numbers, specify the ranges of numbers that may be represented with each notation, along with reasons.

b) Prove the following, using Huntington’s postulates only:

i) A’ + AB = A’ + B

ii) AB+ AB’ = A

Clearly specify the postulates used at each step.

problem 2) Simplify

F(v,w,x,y,z) = Σ(0,2,3,4,7,12,14,18,20,21,26,28,29)

using the tabulation method.

problem 3)a) Design a four input priority encoder

b) Construct a 16 x 1 multiplexer with two 8 x 1 and one 2 x 1 multiplexers.

problem 4)a) With a circuit diagram, describe the working of a D flip flop with a direct reset input.

b) Draw a serial adder. Also, prepare state table and state diagram for the same.

problem 5)a) With a block diagram, describe the working of a 32 K word memory which uses a two dimensional decoding structure.

b)i) List the different specifications of a DAC.

ii) Define and describe each one of the above

problem 6)a) Draw an astable multivibrator using 555 timer which has got a frequency of 5 KHz and duty cycle of 75%.

b) Derive PLA programming table for BCD to Excess-3 code converter.