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Which of the following statements about digital systems are correct?
1. These are easier to design compared to analog systems.
2. These are highly affected by unwanted electrical signals.
3. Accuracy and precision of digital systems are greater when compared with analog systems.
4. The fabrication of digital ICs is complicated and costly than that of analog ICs.
Choose the correct code from the given options:
The advantages of digital systems over analog systems are as follows:
1. Easier to design.
2. Less affected by noise (unwanted electrical signals).
3. More accuracy and precision.
4. Simple and economical fabrication into ICs.
In binary system, we take borrow as 2 for subtraction.
Thus, (1010.01)_{2}  (111.111)_{2} = (0010.011)_{2}.
Assertion (A): The advantage of performing subtraction by the complement method is reduction in the hardware.
Reason (R): Instead of having separate digital circuits for addition and subtraction, only adding circuits are needed for subtraction by complement method.
Both assertion and reason are correct and reason is the correct explanation of assertion because when subtraction is performed using complement method, then instead of subtracting one number from other, the complement of the subtrahend is added to the minued, Thus, subtraction is also performed by adders only as in case of addition. Due to this reason the hardware requirement is reduced while performing subtraction by complement method,
The decimal equivalent of the hexadecimal number (A0F9.0EB)_{16} is
On multiplying the given hexadecimal number with the positional weightage, we get: (A0F9.0EB)_{16}
= (10 x 16^{3}) + (0 x 16^{2}) + (15 x 16^{1}) + (9 x 16^{0}) + (0 x 16^{1}) + (14 x 16^{2})+(11 x 16^{3})
= 40960 + 0 + 240 + 9 + 0 + 0.0546 + 0.0026
= (41209.0572)_{10}
If 100_{b} = 16_{10}, then the value of b would be equal to
On converting 100_{b} to decimal, we have:
1 x b^{2} + 0 x b^{1} + 0 x b^{0} = 16
or, b^{2} = 16
or, b = 4
Consider the following series with a missing number;
10000,121,100, ?, 24, 22, 20
If in the above series, the same integer is expressed in different number systems, the missing number of the series would be equal to
Hence, the missing number is 31 in base 5.
Each of the following arithmetic operations is correct in at least one number system:
(i) 1234 + 5432 = 6666 is valid in any number system with base ≥ 6.
(ii) √41 = 5 is valid in a number system with base 6.
(iii) 302/20 = 12.1 is valid in a number system with base 5.
Out of the above arithmetic operations:
Consider the following statements:
1. In a selfcomplementing code, the code word for the 9's complement of N is the 1’s complement of the codeword for N.
2. Each one of the 4bit BCD codes has 6 illegal states.
3. The Gray code cannot be used for mathematical operations.
4. Excess3 code can be used for mathematical operations.
Which of the statements given above is/are correct?
The ASCII code is a alphanumeric code because it represents alphanumeric information i.e. fetters of the alphabet and decimal numbers as a sequence of 0s and 1s.
Assertion (A): The 2’s complement system has two zeros, a positive 0 (all 0s) and a negative 0 (all 1’s).
Reason (R): The complement of the complement gives the original number
The 1’s complement system has a disadvantage of having two zero representation i.e. a positive 0 (all 0s) and a negative 0 (all 1s). But, the 2's complement system has a unique zero.
Hence, assertion is not a correct statement.
Assertion (A): The computer method of division requires successive subtraction.
Reason (R): The computer method of multiplication requires repeated addition.
Assertion (A): Gray code is sometimes called reflective code.
Reason (R): The n least significant bits for 2n through (2^{n +1} 1) are the mirror images for 0 through (2^{n}1).
Which of the following 4bit binary pairs does not forms a Gray code pair?
The Gray code is a cyclic code in which successive code words in this code differ in one bit position only i.e. it is a unit distance code. In options (a), (b) and (d) both the 4bit binary numbers differ in one bit position only while in option (c) both the 4bit binary numbers differs in two bit positions as shown below.
Hence, option (c) does not forms a gray code pair of two given 4bit binary numbers.
Match ListI (Data representation) with Listll (Range with nbits) and select the correct answer using the codes given below the lists:
List1
A. Signed numbers in 1 ’s complement form
B. Signed magnitude
C. Unsigned magnitude
D. Signed numbers in 2’s complement form
Listll
1. 0 to (2^{n}  1)
2. (2^{n 1}) to + (2^{n 1}  1)
3. (2^{n 1}) to (2^{n 1})
4. (2^{n 1}  1) to + (2^{n 1}  1)
Codes:
A B C D
(a) 3 3 1 2
(b) 1 4 3 4
(c) 2 4 1 3
(d) 4 4 1 2
A number is represented in 2’s complement as (1101)_{2}. It’s equivalent decimal number is
2's complement representation of given number is (1101)_{2}.
Since MSB is 1, therefore the required number must be negative.
1's complement of (1101)_{2} is (0010)_{2}.
2's complement of 0010  (0010)_{2} + (0001)_{2} = (0011)_{2}.
Thus, the required number = 3 (Decimal equivalent of (0011)_{2} = 3).
Match ListI with Listll and select the correct answer using the codes given below the lists:
ListI
A. (345)_{8}
B. (11011.011)_{2}
C. (47)_{16}
ListII
1. (1B.6)_{16}
2. (229)_{10}
3. (107)_{8}
4. (326)_{10}
5. (D8.7)_{16}
Code:
A B C
(a) 2 5 3
(b) 4 3 2
(c) 2 1 3
(d) 4 1 2
Which of the following statements is/are correct in regard to excess3 code?
Multiplication of two binary numbers A and B is 11011. If A = 011, then B is
Let,
B = (b_{3} b_{2}b_{1}b_{0})_{2}
Now,
Thus,
b_{0} = 1
b_{1} + b_{0} = 1 ∴ b_{1} = 0
b_{2} + b_{1} + 0 = 0 ∴ b_{2} = 0
b_{3} + 0 = 1 ∴ b_{3 }= 1
Thus,
B = (b_{3}b_{2}b_{1}b_{0})_{2}
= (1001)_{2}
Which of the following statement is not correct in regard to the “GRAY Code”?
The Gray code is not a BCD code.
Assertion (A): The “XS3 code,” also called “Excess3 code” is a nonweighted BCD code.
Reason (R): In XS3 code, each binary code word is the corresponding 8421 code word plus 0011(3).
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