Kerala Plus One Computer Science Chapter Wise Previous Questions Chapter 2 Data Representation and Boolean Algebra
Question 1.
the complement of the binary number 110111 is …………… (Hint: Use 8 bit form) (March – 2016)
Answer:
Insert 2 zeroes in the left-hand side to make the binary number in the 8 bit form 00110111
To find the l’s complement, change all zeroes to one and all ones to zero.
Hence the answer is 11001000
Question 2.
Express the integer number – 39 in sign and magnitude representation (March – 2016)
Answer:
First find the binary equivalent of 39 for this do the following
In sign and magnitude representation – 39 in 8 bit form is (101 00111)2.
Question 3.
Perform the following number conversions. (Sep – 2016)
a) (110111011.11O11)2 = (….)B
b) (128.25)10 = (……)B
Answer:
a) 110111011.11011
Step 1: Insert a zero in the right side of the above number and divide the number into groups of 3 bits as follows
110 111 011 110 110
Step 2: Write down the corresponding 3 bit binary equivalent of each group
6 7 3 6 6
hence the result is (673.66)8
b) It consists of 2 steps,
Step 1: First convert 128 into octal number for this do the following
Write down the remainders from bottom to top.
(128)10 = (200)8
Step 2 : Then convert .25 into octal number for this do the following
Combine the above two will be the result.
(128.25)10 = (200.2)8
Question 4.
Represent – 38 in 2s complement form. (March – 2017)
Answer:
+38 = 00100110
First take the I ‘s complement for this change all 1 to 0 and all 0 to 1
-38 11011001+
∴ 2’s complement 0f-38 is (11011010)2
Question 5.
18.Draw the logic circuit for the function (Say -2015 (Imp)
f(ab1c) = a.b.c + \(\bar{a}\).b + a\(\bar{b}\) + a.b.\(\bar{c}\)
OR
Prove algebrically
x.y + x.\(\bar{y}\) = x.y. + xz
Answer:
Question 6.
Following are the numbers in various number systems. Two of the numbers are same. Identify them: (March – 2016)
a) (310)8
b) (1010010)2
C) (C8)16
d) (201)10
OR
Consider the following Boolean expression: (B’+A) BA’
Identify the law behind the above expression and prove it using the algebraic method.
(B’+A)’ = BA’
Answer:
Question 7.
With the help of a neat circuit diagram, prove that the NAND gate is a universal gate. (Say – 2016)
Answer:
Question 8.
Boolean expression: (March – 2017)
Using the algebraic method, prove that
Answer:
