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51.

Representation of hexadecimal number (6DE)H indecimal:(a) 6 * 16^2 + 13 * 16^1 + 14 * 16^0(b) 6 * 16^2 + 12 * 16^1 + 13 * 16^0(c) 6 * 16^2 + 11 * 16^1 + 14 * 16^0(d) 6 * 16^2 + 14 * 16^1 + 15 * 16^0The question was posed to me during an online exam.My doubt stems from Number System in section Number System and Codes of Digital Circuits

Answer»

Correct choice is (a) 6 * 16^2 + 13 * 16^1 + 14 * 16^0

The EXPLANATION is: Hexadecimal to Decimal conversion is OBTAINED by multiplying 16 to the power of base index ALONG with the value at that index position.

In hexadecimal NUMBER D & E represents 13 & 14 respectively.

So, 6DE = 6 * 16^2 + 13 * 16^1 + 14 * 16^0.

52.

The largest two digit hexadecimal number is ________(a) (FE)16(b) (FD)16(c) (FF)16(d) (EF)16I had been asked this question during an interview.This intriguing question originated from Number System in portion Number System and Codes of Digital Circuits

Answer»

Right choice is (c) (FF)16

For explanation I would say: (FE)16 is 254 in decimal system, while (FD)16 is 253. (EF)16 is 239 in decimal system. And, (FF)16 is 255. Thus, The largest two-digit hexadecimal number is (FF)16.

53.

The decimal equivalent of the octal number (645)8 is ______(a) (450)10(b) (451)10(c) (421)10(d) (501)10I have been asked this question in an interview for job.My doubt stems from Number System in portion Number System and Codes of Digital Circuits

Answer»

Correct choice is (c) (421)10

Explanation: OCTAL to Decimal conversion is obtained by multiplying 8 to the power of base index along with the VALUE at that index position.

The decimal equivalent of the octal number (645)8is 6 * 8^2 + 4 * 8^1 + 5 * 8^0 = 6 * 64 + 4 * 8 + 5 = 384 + 32 + 5 = (421)10.

54.

An important drawback of binary system is ________(a) It requires very large string of 1’s and 0’s to represent a decimal number(b) It requires sparingly small string of 1’s and 0’s to represent a decimal number(c) It requires large string of 1’s and small string of 0’s to represent a decimal number(d) It requires small string of 1’s and large string of 0’s to represent a decimal numberThe question was asked during a job interview.This intriguing question comes from Number System topic in chapter Number System and Codes of Digital Circuits

Answer»

Right answer is (a) It REQUIRES very large string of 1’s and 0’s to represent a decimal number

The BEST explanation: The most VITAL drawback of BINARY system is that it requires very large string of 1’s and 0’s to represent a decimal number. Hence, Hexadecimal systems are used by processors for calculation purposes as it compresses the long binary strings into small parts.

55.

The decimal equivalent of the binary number (1011.011)2 is ________(a) (11.375)10(b) (10.123)10(c) (11.175)10(d) (9.23)10The question was posed to me in an interview for job.I need to ask this question from Number System topic in section Number System and Codes of Digital Circuits

Answer»

Correct CHOICE is (a) (11.375)10

The best I can EXPLAIN: Binary to DECIMAL conversion is obtained by multiplying 2 to the power of base index ALONG with the value at that index position.

1 * 2^3 + 0 * 2^2 + 1 * 2^1 +1*2^0 + 0 * 2^-1 +1 * 2^-2 + 1 * 2^-3 = (11.375)10

Hence, (1011.011)2 = (11.375)10

56.

The parameter through which 16 distinct values can be represented is known as ________(a) Bit(b) Byte(c) Word(d) NibbleI had been asked this question in an internship interview.My question is from Number System in division Number System and Codes of Digital Circuits

Answer»

The correct CHOICE is (c) Word

The explanation: It can be represented up to 16 different values with the help of a Word. NIBBLE is a combination of four BITS and Byte is a combination of 8 bits. It is “word” that is said to be a collection of 16-bits on most of the systems.

57.

The representation of octal number (532.2)8 in decimal is ________(a) (346.25)10(b) (532.864)10(c) (340.67)10(d) (531.668)10The question was asked in exam.The doubt is from Number System topic in chapter Number System and Codes of Digital Circuits

Answer»

The CORRECT choice is (a) (346.25)10

To elaborate: Octal to Decimal conversion is obtained by MULTIPLYING 8 to the power of base index along with the value at that index POSITION.

(532.2)8 = 5 * 8^2 + 3 * 8^1 + 2 * 8^0 + 2 * 8^-1 = (346.25)10

58.

Any signed negative binary number is recognised by its ________(a) MSB(b) LSB(c) Byte(d) NibbleI had been asked this question during an interview.The above asked question is from Number System in division Number System and Codes of Digital Circuits

Answer» CORRECT option is (a) MSB

The EXPLANATION is: Any negative NUMBER is recognized by its MSB (Most Significant Bit).

If it’s 1, then ít’s negative, else if it’s 0, then positive.
59.

If the decimal number is a fraction then its binary equivalent is obtained by ________ the number continuously by 2.(a) Dividing(b) Multiplying(c) Adding(d) SubtractingThe question was posed to me in an interview for job.The query is from Number System topic in portion Number System and Codes of Digital Circuits

Answer»

Correct choice is (b) MULTIPLYING

For EXPLANATION I would say: On multiplying the decimal number continuously by 2, the binary equivalent is OBTAINED by the collection of the INTEGER part. However, if it’s an integer, then it’s binary equivalent is determined by dividing the number by 2 and collecting the REMAINDERS.