Report on Boolean algebra

Question 1

 

Question 2

Perform the indicated operations in the given number system

a. 

Question 3

a.   Using one’s complement

Table 1:   Using one’s complemented 10110010 -   00011011

b.   Using two’s complement 11100100

Table 2:   Using two’s complement 11100100 -   00011011

Question 4

a.   

Figure 1: logic diagram  

b.  

Figure 2: Logic diagram 

Question no 5

a.      Boolean expression

b.      Corresponding truth table

Table 3:

Question 6

a.      Write the Boolean expression.

b.      Write the truth table.

Table 4: Truth table

Question 7

Simplify the following

Question 8

a.      Logic diagram

c.       Draw the logic diagram of the simplified expression

Figure 3: 

d.      Construct the truth table

Table 5:

For simplified expression it gives

Table 6:

Table 5 and 6 shows that the simplified gate system provides the same operation as Boolean system. Comparison of results is carried out in table 7.

Table 7: Comparison table