# Give the canonical forms of the following function SOP and POS

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```					                       Computer Structure
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.

```
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