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.