problem 1) Add and multiply following numbers in the given base without converting to decimal:
(a) (1203)4 and (332)4
(b) (612.3)8 and (62.6)8
(c) (297)12 and (128)12
problem 2) Show by means of truth tables the proof of De Morgan’s Laws for three variables and distributive law of * over +.
problem 3) The Boolean function: F = xyz + xy’z’ + y’z execute it with:
(a) AND, OR, and NOT Gates
(b) Only OR and Not Gates
(c) Only AND and NOT Gates
problem 4)a) Obtain the simplified expressions in sum of products for the following Boolean Function:
x’z + w’xy’ + w(x’y + xy’)
b) Simplify Boolean function F using don’t-care condition d, in (1) sum of products and (2) product of sums:
F = ACE + A’CD’E’ + A’C’DE, d = DE’ + A’D’E + AD’E’
problem 5)a) Obtain NAND logic diagram of a full-adder from Boolean function:
C = xy + xz + yz and S = C’ (x + y+ z) + xyz
b) Design combinational circuit which accepts three-bit number and generates the output binary number equal to the square of the input number.
problem 6) Design excess-3-to-BCD code converter by using a 4-bit full-adders MSI circuit.
problem 7) Using MSI circuits, construct binary parallel adder to add two 16-bit binary number and label all carries between the MSI circuits.
problem 8) Draw a logic diagram (showing all gates) of a master-slave D flip-flop by using NAND gates.
problem 9)a) Design a BCD counter with JK flip-flops.
b) prepare down the difference between serial and parallel transfer? What kind of register is used in each case?
problem 10)a) Draw a interconnection of I2L gates to form a 2 * 4 decoder.
b) Compute the noise margin of ECL gate.