1Which of the following is the primary characteristic of a digital signal compared to an analog signal?
A.It is continuous in both time and amplitude.
B.It takes on discrete values at discrete time intervals.
C.It is more susceptible to noise degradation.
D.It typically requires less bandwidth than analog signals.
Correct Answer: It takes on discrete values at discrete time intervals.
Explanation:Digital signals are discrete in nature, meaning they occupy specific values (usually binary 0 and 1) at specific time steps, whereas analog signals are continuous.
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2What is the Radix (or base) of the Hexadecimal number system?
A.2
B.8
C.10
D.16
Correct Answer: 16
Explanation:The Hexadecimal system uses 16 distinct symbols ( and ), so its radix is 16.
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3Convert the binary number to its decimal equivalent.
A.11
B.13
C.15
D.9
Correct Answer: 13
Explanation:Using positional weights: .
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4In the hexadecimal number system, the letter 'E' represents which decimal value?
A.11
B.12
C.14
D.15
Correct Answer: 14
Explanation:Hexadecimal digits map as: .
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5Which of the following is a weighted code?
A.Excess-3 Code
B.Gray Code
C.8421 BCD Code
D.ASCII
Correct Answer: 8421 BCD Code
Explanation:In the 8421 BCD code, each bit position has a specific weight ($8, 4, 2, 1$). Excess-3 and Gray codes are non-weighted.
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6What is the primary feature of Gray Code that makes it useful for rotary encoders?
A.It allows for easy arithmetic operations.
B.It is a weighted code.
C.Only one bit changes between successive numbers.
D.It includes built-in error correction.
Correct Answer: Only one bit changes between successive numbers.
Explanation:Gray code is a unit-distance code where only one bit changes state between consecutive values, reducing errors in mechanical switching systems.
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7Calculate the 1's complement of the binary number $101100$.
A.010011
B.010100
C.101101
D.001100
Correct Answer: 010011
Explanation:To find the 1's complement, invert every bit: and . .
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8Calculate the 2's complement of the binary number $0110$.
A.1001
B.1010
C.1000
D.1110
Correct Answer: 1010
Explanation:The 2's complement is found by taking the 1's complement and adding 1. 1's complement of $0110$ is $1001$. .
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9Convert the decimal number $25$ to Binary.
A.11001
B.10011
C.11100
D.10101
Correct Answer: 11001
Explanation:, which is .
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10Which of the following represents the range of a signed decimal number that can be represented by bits using 2's complement form?
A. to
B. to
C. to
D.$0$ to
Correct Answer: to
Explanation:In 2's complement, there is one more negative number than positive number because zero is considered positive in the sign bit context. For example, 8 bits: -128 to +127.
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11Convert the Octal number to Binary.
A.111101
B.111110
C.110101
D.101111
Correct Answer: 111101
Explanation:Convert each octal digit to a 3-bit binary equivalent. , . Result: $111101$.
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12The BCD (Binary Coded Decimal) representation of the decimal number $39$ is:
A.00111001
B.00100111
C.100111
D.00111111
Correct Answer: 00111001
Explanation:In 8421 BCD, each decimal digit is represented by 4 bits. , . Combined: .
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13What is the Hamming Distance between the codes $10101$ and $10011$?
A.1
B.2
C.3
D.4
Correct Answer: 2
Explanation:Hamming distance is the number of positions at which the corresponding bits are different. . There are two 1s in the result, so the distance is 2.
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14How many parity bits are required to correct a single bit error for a 4-bit data word using Hamming Code?
A.2
B.3
C.4
D.1
Correct Answer: 3
Explanation:Using the formula , where . If , . Thus, 3 parity bits are required.
17Which of the following is a self-complementing code?
A.8421 BCD
B.Excess-3 Code
C.Gray Code
D.ASCII
Correct Answer: Excess-3 Code
Explanation:In Excess-3 code, the 9's complement of a decimal number can be obtained by simply taking the 1's complement of the binary code. This makes it self-complementing.
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18What is the result of converting the binary number $11011.101$ to octal?
A.33.5
B.32.5
C.63.4
D.27.5
Correct Answer: 33.5
Explanation:Group bits in threes from the decimal point. Left: , (Result 33). Right: (Result .5). Total: .
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19In IEEE 754 Single Precision floating point representation, how many bits are allocated for the Exponent?
A.8 bits
B.11 bits
C.23 bits
D.32 bits
Correct Answer: 8 bits
Explanation:Single precision (32-bit) consists of 1 sign bit, 8 exponent bits, and 23 mantissa/fraction bits.
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20What does a Parity Bit essentially check?
A.The magnitude of the data.
B.If the number of 1s in the data is odd or even.
C.The sign of the number.
D.The position of the error.
Correct Answer: If the number of 1s in the data is odd or even.
Explanation:A parity bit is added to ensure the total number of 1s in the string is either even (Even Parity) or odd (Odd Parity). It detects single-bit errors.
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21Convert the Binary code $1010$ to Gray code.
A.1100
B.1111
C.1001
D.1110
Correct Answer: 1111
Explanation:MSB remains same (1). Next bit = . Next = . Next = . Result: $1111$.
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22In the Octal number system, what is the result of ?
A.18
B.20
C.10
D.21
Correct Answer: 20
Explanation:In Octal, digits range . , which is represented as . So, : carry 1. . Result .
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23Which of the following bit patterns represents an INVALID code in 8421 BCD?
A.1000
B.0111
C.1100
D.0010
Correct Answer: 1100
Explanation:BCD uses 4 bits to represent decimal 0-9 ($0000$ to $1001$). Binary values $1010$ (10) through $1111$ (15) are invalid. $1100$ is 12, hence invalid.
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24What is the 9's complement of the decimal number $27$?
A.72
B.82
C.73
D.63
Correct Answer: 72
Explanation:To find 9's complement, subtract each digit from 9. .
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25Fixed-point representation is best described as:
A.A system where the decimal point can 'float' to any position.
B.A system where the position of the radix point is fixed.
C.A system used only for integers.
D.A system used exclusively for analog signals.
Correct Answer: A system where the position of the radix point is fixed.
Explanation:In fixed-point notation, the gap between the integer part and the fractional part (the radix point) is fixed at a specific position.
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26Perform the Hexadecimal subtraction: .
A.1D
B.2D
C.13
D.23
Correct Answer: 1D
Explanation: requires a borrow. Borrow 1 from 4 (making it 3). The becomes . , which is . . Result: .
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27What is the 10's complement of the decimal number $456$?
A.543
B.544
C.454
D.554
Correct Answer: 544
Explanation:10's complement = 9's complement + 1. 9's complement of 456 is . .
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28Which code is also known as the 'Reflected Code'?
A.BCD Code
B.Gray Code
C.Hamming Code
D.ASCII
Correct Answer: Gray Code
Explanation:Gray code is constructed by reflecting the binary sequence, hence the name Reflected Code.
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29In a positional number system, the value of a digit is determined by:
A.The digit itself only.
B.The position of the digit relative to the radix point.
C.The total number of digits.
D.The parity of the number.
Correct Answer: The position of the digit relative to the radix point.
Explanation:In positional systems (like decimal or binary), the value is the digit multiplied by the base raised to the power of its position index.
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30What is the minimum number of bits required to represent the decimal number $32$ in binary?
A.5
B.6
C.7
D.4
Correct Answer: 6
Explanation:$32$ in binary is $100000$, which requires 6 bits.
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31If an Odd Parity system receives the data $1011001$ (7 bits), is there an error detected?
A.Yes, because the number of 1s is even (4).
B.No, because the number of 1s is even (4).
C.Yes, because the number of 1s is odd (3).
D.No, parity cannot check this.
Correct Answer: Yes, because the number of 1s is even (4).
Explanation:The received data has four 1s. In an Odd Parity system, the total number of 1s must be odd. Since 4 is even, an error is detected.
33To represent the decimal number in 4-bit Sign-Magnitude form:
A.1101
B.1011
C.1110
D.0101
Correct Answer: 1101
Explanation:In Sign-Magnitude, the MSB is the sign ($1$ for negative) and the remaining bits are magnitude. Magnitude of $5$ is $101$. Result: $1101$.
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34The 15's complement of the Hexadecimal digit is:
A.3
B.4
C.2
D.D
Correct Answer: 3
Explanation:15's complement is found by subtracting the digit from (15). .
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35Which of the following equations correctly describes the relationship for checking overflow when adding two signed numbers with the same sign (where is carry into sign bit, is carry out of sign bit)?
A.Overflow =
B.Overflow =
C.Overflow =
D.Overflow = 1
Correct Answer: Overflow =
Explanation:Overflow in 2's complement addition occurs if the carry into the sign bit and the carry out of the sign bit are different ( operation).
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36What is the equivalent of binary $101010$ in Excess-3 code?
A.0111 0101
B.1000 0110
C.0011 1100
D.0110 0101
Correct Answer: 0111 0101
Explanation:First convert Binary $101010$ to Decimal . Convert Decimal digits to Excess-3. , . Result .
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37Which number system is most commonly used for addressing memory locations in computer assembly language?
A.Octal
B.Hexadecimal
C.Gray Code
D.BCD
Correct Answer: Hexadecimal
Explanation:Hexadecimal is compact and maps directly to 4-bit nibbles, making it ideal for representing large binary addresses (e.g., 32-bit or 64-bit).
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38Compute the value of if .
A.2
B.4
C.5
D.10
Correct Answer: 5
Explanation:.
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39The checksum method is primarily used for:
A.Error Correction
B.Error Detection
C.Encryption
D.Data Compression
Correct Answer: Error Detection
Explanation:Checksums are calculated values attached to data to verify its integrity. If the calculated checksum of received data doesn't match the sent checksum, an error is detected.
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40In binary arithmetic, ?
A.0
B.1
C.10
D.11
Correct Answer: 0
Explanation:Basic binary subtraction: .
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41Convert to Binary.
A.0.1011
B.0.1101
C.0.1010
D.0.0111
Correct Answer: 0.1011
Explanation:; ; ; . Read downwards: $0.1011$.
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42Which of the following is an alphanumeric code?
A.BCD
B.ASCII
C.Excess-3
D.Gray Code
Correct Answer: ASCII
Explanation:ASCII (American Standard Code for Information Interchange) represents letters, numbers, and symbols, making it an alphanumeric code.
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43What is the base of the system if ?
A.4
B.5
C.6
D.8
Correct Answer: 5
Explanation:Unit column: . Since result is 0, . This implies the base is 5.
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44In a 3-bit binary system, what is the sequence of Gray codes corresponding to decimal 0, 1, 2, 3?
A.000, 001, 010, 011
B.000, 001, 011, 010
C.000, 010, 011, 001
D.000, 100, 010, 001
Correct Answer: 000, 001, 011, 010
Explanation:Decimal 2 in binary is 010, in Gray is 011. Decimal 3 in binary is 011, in Gray is 010.
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45Which term describes the least significant bit (LSB)?
A.The bit with the highest weighting.
B.The leftmost bit in a standard binary string.
C.The bit with the weight .
D.The sign bit.
Correct Answer: The bit with the weight .
Explanation:The LSB is the rightmost bit in an integer, representing the lowest weight ().
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46The representation of decimal $0$ in 1's complement has how many forms?
A.1 (+0)
B.2 (+0 and -0)
C.3
D.Infinite
Correct Answer: 2 (+0 and -0)
Explanation:In 1's complement (8-bit), is $00000000$ and is $11111111$. This double representation of zero is a drawback of 1's complement.
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47What is the decimal equivalent of the largest number that can be stored in an 8-bit unsigned binary register?
A.127
B.128
C.255
D.256
Correct Answer: 255
Explanation:Max value for bits is . For 8 bits: .
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48When converting Hexadecimal to Octal, it is often easiest to convert to which intermediate system first?
A.Decimal
B.Binary
C.BCD
D.ASCII
Correct Answer: Binary
Explanation:Hex maps to 4 bits, Octal maps to 3 bits. Converting Hex Binary regrouping bits for Octal is the most efficient method.
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49Which of these codes is a Weighted Code where the weights are 2, 4, 2, 1?
A.Excess-3
B.Gray Code
C.2421 Code
D.5421 Code
Correct Answer: 2421 Code
Explanation:The 2421 code is a self-complementing weighted code where the weights of the bit positions are 2, 4, 2, and 1 respectively.
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50In floating point notation, what is the purpose of the Bias added to the exponent?
A.To make the mantissa always positive.
B.To represent negative exponents without using a sign bit for the exponent.
C.To increase the precision.
D.To detect errors.
Correct Answer: To represent negative exponents without using a sign bit for the exponent.
Explanation:Biasing the exponent shifts the range of values so that they are all non-negative integers, allowing simple magnitude comparison of exponents.