Binary to Gray and Gray to binary code conversion
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The first Gray bit is . XOR adjacent binary bits: , , and . Thus, the Gray code is .
Incorrect! Try again.
4What is the binary equivalent of Gray code ?
Binary to Gray and Gray to binary code conversion
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The first binary bit is . Each next binary bit is the XOR of the previous binary bit and the current Gray bit, giving .
Incorrect! Try again.
5What is the Excess-3 code for decimal digit ?
Excess-3
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Excess-3 code is formed by adding to the decimal digit. For , , and in binary is .
Incorrect! Try again.
6Which decimal digit is represented by the Excess-3 code ?
Excess-3
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Subtract from the binary value . Therefore, the represented digit is .
Incorrect! Try again.
7Which BCD code represents the decimal digit ?
BCD
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
In BCD, each decimal digit is represented separately using four bits. Decimal is represented as .
Incorrect! Try again.
8How is decimal number represented in BCD?
BCD
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The digit is coded as and the digit as , so is in BCD.
Incorrect! Try again.
9What is the 1's complement of binary number ?
Compliments
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The 1's complement is obtained by changing every to and every to . Thus, becomes .
Incorrect! Try again.
10What is the 2's complement of the 4-bit binary number ?
Compliments
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The 1's complement of is . Adding gives the 2's complement, .
Incorrect! Try again.
11What is the result of binary addition ?
Binary arithmetic
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The binary values are and . Their sum is , which is .
Incorrect! Try again.
12What is the result of binary subtraction ?
Binary arithmetic
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The binary values are and . Their difference is , which is .
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13In 2's complement subtraction, what is added to the minuend?
Addition and subtraction using 2's complement
Easy
A.The sign bit
B.The parity bit
C.The 2's complement
D.The 1's complement
Correct Answer: The 2's complement
Explanation:
Subtraction using 2's complement is performed by adding the 2's complement of the subtrahend to the minuend.
Incorrect! Try again.
14Using 4-bit 2's complement, what is the result of ?
Addition and subtraction using 2's complement
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The 2's complement of is . Adding gives ; discard the carry to obtain .
Incorrect! Try again.
15Which logic gate produces an output of only when all its inputs are ?
Logic gates
Easy
A.NOT gate
B.OR gate
C.XOR gate
D.AND gate
Correct Answer: AND gate
Explanation:
An AND gate gives an output of only when every input is .
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16What is the output of a NOT gate when its input is ?
Logic gates
Easy
A.
B.
C.Undefined
D.The same input
Correct Answer:
Explanation:
A NOT gate inverts its input. Therefore, an input of produces an output of .
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17According to the Boolean identity law, what is ?
Boolean algebra
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The identity law for OR states that .
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18What does SOP stand for in Boolean algebra?
SOP and POS
Easy
A.Sum of Powers
B.Sum of Products
C.Sequence of Products
D.Set of Parameters
Correct Answer: Sum of Products
Explanation:
SOP means Sum of Products, where product terms are formed using AND operations and then added using OR operations.
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19Which expression is in Product of Sums form?
SOP and POS
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
POS consists of products of sum terms. The expression has two sum terms multiplied together.
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20What is the main purpose of a Karnaugh map?
K-Map (up to 4 variables)
Easy
A.To generate clock pulses
B.To simplify Boolean expressions
C.To store binary data
D.To convert decimal numbers
Correct Answer: To simplify Boolean expressions
Explanation:
A Karnaugh map provides a visual method for grouping terms and simplifying Boolean expressions.
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21What is the binary equivalent of the decimal number ?
Number system conversion
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
, so the corresponding binary representation is .
Incorrect! Try again.
22Convert the hexadecimal number to decimal.
Number system conversion
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
.
Incorrect! Try again.
23What is the binary equivalent of the Gray code ?
Binary to Gray and Gray to binary code conversion
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The first binary bit is . Subsequent bits are obtained by XORing the previous binary bit with the current Gray bit, giving .
Incorrect! Try again.
24Convert the binary number into Gray code.
Binary to Gray and Gray to binary code conversion
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The Gray code is formed as , followed by XORs of adjacent binary bits: , resulting in .
Incorrect! Try again.
25What is the Excess-3 representation of the decimal number ?
Excess-3
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Add to each decimal digit: and . Their 4-bit binary forms are and , giving .
Incorrect! Try again.
26The BCD code represents which decimal number?
BCD
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The groups and represent decimal digits and , respectively. Therefore, the number is .
Incorrect! Try again.
27What is the 1's complement of the 8-bit binary number ?
Compliments
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The 1's complement is obtained by changing every to and every to , producing .
Incorrect! Try again.
28What is the result of the binary addition ?
Binary arithmetic
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
and . Their sum is , which is .
Incorrect! Try again.
29Using 5-bit 2's complement arithmetic, what is ?
Addition and subtraction using 2's complement
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
represents and represents . Thus, , represented as .
Incorrect! Try again.
30Using 5-bit signed 2's complement arithmetic, what is the result of ?
Addition and subtraction using 2's complement
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The bitwise addition gives . In 5-bit signed arithmetic, this result indicates overflow because two positive numbers produced a negative sign bit.
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31A NAND gate has inputs and . What is its output?
Logic gates
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
A NAND gate is the complement of an AND gate. Since , the NAND output is .
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32Which gate produces an output of only when its two inputs are different?
Logic gates
Medium
A.XNOR gate
B.XOR gate
C.OR gate
D.AND gate
Correct Answer: XOR gate
Explanation:
The XOR gate outputs when exactly one input is , so its inputs must be different.
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33Simplify the Boolean expression .
Boolean algebra
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
By the absorption law, . The term is already included whenever .
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34Using De Morgan's theorem, simplify .
Boolean algebra
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
De Morgan's theorem states that the complement of an OR operation equals the AND of the complements: .
Incorrect! Try again.
35Which of the following is in standard Sum of Products (SOP) form?
SOP and POS
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
SOP form consists of multiple product terms connected by OR operations. The expression has this structure.
Incorrect! Try again.
36Which of the following is in Product of Sums (POS) form?
SOP and POS
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
POS form consists of sum terms enclosed in parentheses and connected by AND operations. Thus, is in POS form.
Incorrect! Try again.
37Using a 3-variable K-map, simplify .
K-Map (up to 4 variables)
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The minterms are exactly the combinations where . Therefore, the simplified function is .
Incorrect! Try again.
38Using a 4-variable K-map with variables ordered as , simplify .
K-Map (up to 4 variables)
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
For all listed minterms, and , while and vary. The common implicant is therefore .
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39Using a 4-variable K-map, simplify .
K-Map (up to 4 variables)
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The four minterms share and , while and vary. Hence, the simplified expression is .
Incorrect! Try again.
40Simplify the Boolean expression .
Boolean algebra
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Applying the distributive and absorption laws, .
Incorrect! Try again.
41Convert the hexadecimal number to its equivalent octal representation.
Number system conversion
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Using binary as an intermediate, . Regrouping in sets of three bits gives .
Incorrect! Try again.
42Which base-7 representation is exactly equivalent to ?
Number system conversion
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
. The integer part is , while repeated multiplication of by continually produces the digit .
Incorrect! Try again.
43The 6-bit reflected Gray word is received with its third bit from the left inverted. What decimal value is represented by the corrupted Gray word?
Binary to Gray and Gray to binary code conversion
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Inverting the third bit gives Gray word . Successive prefix XOR operations produce binary , which equals .
Incorrect! Try again.
44What is the binary equivalent of the reflected Gray-code word ?
Binary to Gray and Gray to binary code conversion
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The most significant binary bit equals the first Gray bit. Each remaining binary bit is the XOR of the previous binary bit and the current Gray bit, giving .
Incorrect! Try again.
45Two decimal numbers are represented in Excess-3 code as and . What is the Excess-3 representation of their decimal sum?
Excess-3
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The code words represent and , respectively. Their sum is , whose Excess-3 digits are , , and .
Incorrect! Try again.
46Two BCD digits, and , are added along with an input carry of . After decimal correction, what are the output carry and BCD sum digit?
BCD
Hard
A.Carry , digit
B.Carry , digit
C.Carry , digit
D.Carry , digit
Correct Answer: Carry , digit
Explanation:
The decimal operation is . Therefore, the BCD result has an output carry of and a units digit of , encoded as .
Incorrect! Try again.
47Using 8-bit one's-complement arithmetic, what bit pattern results from before interpreting its sign?
Compliments
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
. In 8-bit one's complement, is , so is its bitwise complement, .
Incorrect! Try again.
48A fixed-point octal register has six integer digits and two fractional digits. What is the 8's complement of in this register?
Compliments
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The 7's complement is . Adding one unit in the least significant position, , gives the 8's complement .
Incorrect! Try again.
49Evaluate the unsigned binary product .
Binary arithmetic
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
and . Their product is , which is .
Incorrect! Try again.
50When the unsigned binary number is divided by , what are the quotient and remainder?
Binary arithmetic
Hard
A.Quotient , remainder
B.Quotient , remainder
C.Quotient , remainder
D.Quotient , remainder
Correct Answer: Quotient , remainder
Explanation:
and . Since , the quotient is and the remainder is .
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51In 8-bit two's-complement arithmetic, what stored result and overflow status are obtained for ?
Addition and subtraction using 2's complement
Hard
A., overflow occurs
B., no overflow occurs
C., no overflow occurs
D., overflow occurs
Correct Answer: , overflow occurs
Explanation:
The mathematical result is , outside the 8-bit signed range to . The stored pattern wraps to , and signed overflow is set.
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52A 6-bit two's-complement processor evaluates . What result is stored, and does signed overflow occur?
Addition and subtraction using 2's complement
Hard
A., overflow occurs
B., no overflow occurs
C., no overflow occurs
D., overflow occurs
Correct Answer: , overflow occurs
Explanation:
The true result is , below the 6-bit minimum of . Modulo , it is stored as , with signed overflow.
Incorrect! Try again.
53A circuit uses only NAND gates: , , , and . Which function does implement?
Logic gates
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The intermediate NAND gates generate the two unequal-input terms. The final NAND combines them to produce .
Incorrect! Try again.
54A circuit uses only NOR gates: , , , and . Which function does implement?
Logic gates
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Here and . Thus , which is the XNOR function .
Incorrect! Try again.
55Simplify using Boolean algebra.
Boolean algebra
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
By the consensus theorem in product-of-sums form, is the consensus factor of and and is therefore redundant.
Incorrect! Try again.
56Which expression is equivalent to ?
Boolean algebra
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The term is the consensus term of and . Removing it does not change the function, so .
Incorrect! Try again.
57Given , which is its canonical POS representation?
SOP and POS
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Canonical POS lists the maxterm indices where . These are precisely the indices absent from the given minterm list.
Incorrect! Try again.
58For three variables ordered as , convert to canonical SOP form.
SOP and POS
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The product is for input combinations , , , and , corresponding to minterms , , , and .
Incorrect! Try again.
59Use a 4-variable K-map to minimize in SOP form.
K-Map (up to 4 variables)
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
An octet containing gives . A group containing gives , so .
Incorrect! Try again.
60A minimal two-level SOP realization of is , but it has a static-1 hazard. Which SOP expression is hazard-free?
K-Map (up to 4 variables)
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
When , changing transfers coverage between and . Adding the consensus implicant provides overlapping K-map coverage and removes the static-1 hazard.
Incorrect! Try again.
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