Number Systems and Codes Questions and Answers

Q: What is the octal equivalent of (F3B1) hexadecimal number?

The octal equivalent is 171661.Write each hex digit as 4 bits, then regroup the bits in threes from the right:\[ \begin{aligned} \text{F3B1} &= 1111\ 0011\ 1011\ 0001 \\ &= 1\ 111\ 001\ 110\ 110\ 001 \\ &= 1\,7\,1\,6\,6\,1 \end{aligned} \]As a check, both equal 62385 in decimal. The other options do not convert back to F3B1.Converting through binary is the safe route between hexadecimal and octal, because each hex digit is exactly four bits and each octal digit exactly three.

Q: The sum of three binary numbers 10110.10, 11010.01 and 10101.11 in decimal system is :

The sum is 70.50.Convert each number, remembering that the first two places after the binary point are worth 1/2 and 1/4:\[ \begin{aligned} 10110.10 &= 22.50 \\ 11010.01 &= 26.25 \\ 10101.11 &= 21.75 \\ \text{sum} &= 70.50 \end{aligned} \]70.75 and 70.25 come from misreading one fractional part, and 69.50 from dropping a carry.A useful check is that each binary fraction place halves in value: .1 is 0.5, .01 is 0.25 and .11 is 0.75.

Q: The octal number system has a base of

The octal number system has a base of 8.Octal uses the eight digits 0 to 7, and each place is worth a power of 8. Because 8 = 23, each octal digit stands for exactly three binary digits, which is why octal was used as a shorthand for binary.Base 2 is binary, base 10 is the ordinary decimal system, and base 16 is hexadecimal, which uses 0 to 9 and A to F.

Q: Convert (15)10 to hexadecimal

(15)10 in hexadecimal is F.Hexadecimal uses sixteen digits: 0 to 9 for zero to nine, then A, B, C, D, E and F for ten to fifteen. Fifteen is less than sixteen, so it needs only one hexadecimal digit, and that digit is F.E is fourteen. 10 in hexadecimal is sixteen (one sixteen and no units). 'IF' is not a hexadecimal numeral, since I is not a hexadecimal digit; 1F would be thirty-one.

Q: What is the binary equivalent of the decimal number \((25)_{10}\) ?

The binary form is \((11001)_{2}\).Write 25 as a sum of powers of two, or divide by 2 repeatedly and read the remainders upward.\[ \begin{aligned} 25 &= 16 + 8 + 1 \\ &= 2^{4} + 2^{3} + 2^{0} \\ &= (11001)_{2} \end{aligned} \]Check the others: \((11011)_{2} = 27\), \((10011)_{2} = 19\) and \((10001)_{2} = 17\). Only 11001 gives 25.

Q: What is the OCTAL equivalent of the HEXADECIMAL number \((ADF)_{16}\) ?

The octal equivalent is \((5337)_{8}\).Convert through binary: each hexadecimal digit becomes four bits, then regroup into threes from the right for octal.\[ \begin{aligned} A\,D\,F &= 1010\ 1101\ 1111 \\ &= 101\ 011\ 011\ 111 \\ &= 5\ 3\ 3\ 7 \end{aligned} \]Check in decimal: \(ADF_{16} = 10 \times 256 + 13 \times 16 + 15 = 2783\), and \(5 \times 512 + 3 \times 64 + 3 \times 8 + 7 = 2783\). The other options differ by a digit and fail this check.

Q: Knowledge of binary number system is required for the designers of computers and other digital systems because

The reason is that the devices used in these systems operate in binary.Digital circuits are built from switching elements, transistors, gates and flip-flops, that are reliably in one of two states, on or off, high or low. Every number, character and instruction a computer handles is therefore stored and processed as patterns of 0s and 1s, and a designer must work in that system.Ease of learning binary, Boolean algebra or binary codes is not the reason. Binary is used because the hardware has two states, whatever its difficulty.

Q: Digital representations of numerical values of quantities may BEST be described as having characteristics

Digital representations vary in discrete steps in proportion to the values they represent.A digital quantity can take only a fixed set of values, so as the measured quantity changes the representation jumps from one value to the next, like the digits of a counter. A 4-bit code, for instance, has exactly 16 possible values.Changing continuously, or varying smoothly over a continuous range or in direct proportion, describes analog representation, such as the needle of a meter or the height of mercury in a thermometer.

11.

What is the octal equivalent of (F3B1) hexadecimal number?

A.178543
B.172101
C.171661
D.171541

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: C

The octal equivalent is 171661.

Write each hex digit as 4 bits, then regroup the bits in threes from the right:

\[ \begin{aligned} \text{F3B1} &= 1111\ 0011\ 1011\ 0001 \\ &= 1\ 111\ 001\ 110\ 110\ 001 \\ &= 1\,7\,1\,6\,6\,1 \end{aligned} \]

As a check, both equal 62385 in decimal. The other options do not convert back to F3B1.

Converting through binary is the safe route between hexadecimal and octal, because each hex digit is exactly four bits and each octal digit exactly three.

Discuss in Forum

12.

The sum of three binary numbers 10110.10, 11010.01 and 10101.11 in decimal system is :

A.70.75
B.70.25
C.70.50
D.69.50

Exam Year(s)

Tripura Public Service Commission - 2025,

Answer: C

The sum is 70.50.

Convert each number, remembering that the first two places after the binary point are worth 1/2 and 1/4:

\[ \begin{aligned} 10110.10 &= 22.50 \\ 11010.01 &= 26.25 \\ 10101.11 &= 21.75 \\ \text{sum} &= 70.50 \end{aligned} \]

70.75 and 70.25 come from misreading one fractional part, and 69.50 from dropping a carry.

A useful check is that each binary fraction place halves in value: .1 is 0.5, .01 is 0.25 and .11 is 0.75.

Discuss in Forum

13.

The octal number system has a base of

A.2
B.8
C.10
D.16

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: B

The octal number system has a base of 8.

Octal uses the eight digits 0 to 7, and each place is worth a power of 8. Because 8 = 2³, each octal digit stands for exactly three binary digits, which is why octal was used as a shorthand for binary.

Base 2 is binary, base 10 is the ordinary decimal system, and base 16 is hexadecimal, which uses 0 to 9 and A to F.

Discuss in Forum

14.

Convert (15)₁₀ to hexadecimal

A.E
B.IF
C.F
D.10

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

(15)₁₀ in hexadecimal is F.

Hexadecimal uses sixteen digits: 0 to 9 for zero to nine, then A, B, C, D, E and F for ten to fifteen. Fifteen is less than sixteen, so it needs only one hexadecimal digit, and that digit is F.

E is fourteen. 10 in hexadecimal is sixteen (one sixteen and no units). 'IF' is not a hexadecimal numeral, since I is not a hexadecimal digit; 1F would be thirty-one.

Discuss in Forum

15.

What is the binary equivalent of the decimal number \((25)_{10}\) ?

A.\((11011)_{2}\)
B.\((10011)_{2}\)
C.\((11001)_{2}\)
D.\((10001)_{2}\)

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: C

The binary form is \((11001)_{2}\).

Write 25 as a sum of powers of two, or divide by 2 repeatedly and read the remainders upward.

\[ \begin{aligned} 25 &= 16 + 8 + 1 \\ &= 2^{4} + 2^{3} + 2^{0} \\ &= (11001)_{2} \end{aligned} \]

Check the others: \((11011)_{2} = 27\), \((10011)_{2} = 19\) and \((10001)_{2} = 17\). Only 11001 gives 25.

Discuss in Forum

16.

What is the OCTAL equivalent of the HEXADECIMAL number \((ADF)_{16}\) ?

A.\((5467)_{8}\)
B.\((6517)_{8}\)
C.\((5437)_{8}\)
D.\((5337)_{8}\)

Exam Year(s)

Tripura Public Service Commission - 2026,

Answer: D

The octal equivalent is \((5337)_{8}\).

Convert through binary: each hexadecimal digit becomes four bits, then regroup into threes from the right for octal.

\[ \begin{aligned} A\,D\,F &= 1010\ 1101\ 1111 \\ &= 101\ 011\ 011\ 111 \\ &= 5\ 3\ 3\ 7 \end{aligned} \]

Check in decimal: \(ADF_{16} = 10 \times 256 + 13 \times 16 + 15 = 2783\), and \(5 \times 512 + 3 \times 64 + 3 \times 8 + 7 = 2783\). The other options differ by a digit and fail this check.

Discuss in Forum

17.

Knowledge of binary number system is required for the designers of computers and other digital systems because

A.it is easy to learn binary number system
B.it is easy to learn Boolean algebra
C.it is easy to use binary codes
D.the devices used in this systems operate in binary

Exam Year(s)

Tripura Public Service Commission - 2019,

Answer: D

The reason is that the devices used in these systems operate in binary.

Digital circuits are built from switching elements, transistors, gates and flip-flops, that are reliably in one of two states, on or off, high or low. Every number, character and instruction a computer handles is therefore stored and processed as patterns of 0s and 1s, and a designer must work in that system.

Ease of learning binary, Boolean algebra or binary codes is not the reason. Binary is used because the hardware has two states, whatever its difficulty.

Discuss in Forum

18.

Digital representations of numerical values of quantities may BEST be described as having characteristics

A.that are difficult to interpret because they are continuously changing
B.that vary constantly over a continuous range of values
C.that vary in constant and direct proportion to the values they represent
D.that vary in discrete steps in proportion to the values they represent

Exam Year(s)

Tripura Public Service Commission - 2019,

Answer: D

Digital representations vary in discrete steps in proportion to the values they represent.

A digital quantity can take only a fixed set of values, so as the measured quantity changes the representation jumps from one value to the next, like the digits of a counter. A 4-bit code, for instance, has exactly 16 possible values.

Changing continuously, or varying smoothly over a continuous range or in direct proportion, describes analog representation, such as the needle of a meter or the height of mercury in a thermometer.

Discuss in Forum

Loading…

Topics

Other Subjects

Tags: Number Systems and Codes Questions and Answers || Number Systems and Codes MCQ Questions and Answers || Number Systems and Codes GK Questions and Answers || Number Systems and Codes GK MCQ Questions || Number Systems and Codes Multiple Choice Questions and Answers || Number Systems and Codes GK || GK on Number Systems and Codes || Digital Electronics Questions and Answers || Digital Electronics MCQ Questions and Answers || Digital Electronics GK Questions and Answers || GK on Digital Electronics

Number Systems and Codes Questions and Answers

Topics

Other Subjects

About Us

Stay informed about all important Dates & Notifications