Exercise Number 2
1. Give the canonical forms of the following function (SOP and POS):
F(W,X,Y,Z) = X'W (Y'Z + X') + [ X(XOR)Y ]
2. The gate L has 4 inputs:
L(x1,x2,x3,x4) = x2x3 (x1 + x4)
Use the variables, their complements, 3 gates of type L and one OR gate
(with 3 inputs) to implement the function:
F(w,x,y,z) = SIGMA ( 0,1,6,9,10,11,14,15 )
3. f1 and f2 are functions of the variables x and y which are functions of
a and c :
f1= ab + b'c' = x' ; f2 = a'(bc' +b'c) = xy'
Find the minimal form of x and y as functions of a , b and c.
4. Obtain the minimal form of the function
f(a,b,c,d) = SIGMA (1,3,4,5,6,7,10,12,13) + SIGMA d (2,9,15)
('SIGMA d' stands for the don't care combinations)
5. Design a system which performs a full addition of two decimal digits,
which are given in BCD code. The answer should be in BCD code.
Use Full Adder units and minimum number of gates.
6. Design a system which operates as follows:
For a control value k=0 it performs an addition of x and y ,
when k=1 it performs the subtraction x-y.
x = x2x1x0
y = y2y1y0
x2 and y2 are the sign bits. Use Half Adders and Full Adders.
(You can choose the representation of the signed numbers).
7. X is a 4 bit binary number in the two's complement representation.
Obtain the complement of X.
Use H.A. units and NOT gates only.
8. Use only one unit of Multiplexer of order 4*1 to obtain the function:
f(w,x,y,z) = SIGMA(2,5,6,7,12,13) + SIGMA d (3,10,14,15)
Constants and logical gates are not available.