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Quiz: Number Systems and Binary Arithmetic

Test your understanding of number systems, binary arithmetic, and encoding schemes with these questions.

1. What is the decimal equivalent of the binary number 10110?

  1. 18
  2. 22
  3. 26
  4. 30
Show Answer

The correct answer is B. To convert binary 10110 to decimal, add the position values where there is a 1: 16 + 4 + 2 = 22. The positions are (from right to left): 2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16.

Concept Tested: Binary to Decimal Conversion

2. Which number system uses base 16 and digits 0-9 plus A-F?

  1. Binary
  2. Octal
  3. Hexadecimal
  4. BCD
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The correct answer is C. Hexadecimal (hex) is a base-16 number system that uses digits 0-9 for values 0-9 and letters A-F for values 10-15. It provides a compact way to represent binary values since each hex digit corresponds to exactly 4 binary bits.

Concept Tested: Hexadecimal Numbers

3. What is the result of the binary addition 1011 + 0110?

  1. 10001
  2. 10010
  3. 10011
  4. 10101
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The correct answer is A. Adding 1011 (11) + 0110 (6) = 10001 (17). Working right to left: 1+0=1, 1+1=10 (write 0, carry 1), 0+1+1=10 (write 0, carry 1), 1+0+1=10 (write 0, carry 1), carry 1.

Concept Tested: Binary Addition

4. In two's complement representation using 8 bits, what decimal value does 11111111 represent?

  1. 255
  2. -1
  3. -127
  4. 0
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The correct answer is B. In two's complement, 11111111 represents -1. The MSB (leftmost bit) being 1 indicates a negative number. To find the magnitude, invert all bits (00000000) and add 1 (00000001 = 1), so the value is -1.

Concept Tested: Two's Complement

5. What is the primary advantage of Gray code over standard binary?

  1. It uses fewer bits to represent the same values
  2. Only one bit changes between consecutive values
  3. It can represent larger numbers
  4. It is easier to convert to decimal
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The correct answer is B. Gray code is designed so that consecutive values differ by exactly one bit. This property eliminates multi-bit transition errors in applications like rotary encoders and reduces glitches when crossing clock domains.

Concept Tested: Gray Code

6. How would you convert decimal 45 to binary using repeated division by 2?

  1. Divide by 2 repeatedly and read remainders top to bottom
  2. Divide by 2 repeatedly and read remainders bottom to top
  3. Multiply by 2 repeatedly and record the integer parts
  4. Subtract powers of 2 starting from the largest
Show Answer

The correct answer is B. To convert decimal to binary, repeatedly divide by 2 and record the remainders. The remainders, read from bottom to top (last to first), form the binary number. For 45: 45÷2=22 R1, 22÷2=11 R0, 11÷2=5 R1, 5÷2=2 R1, 2÷2=1 R0, 1÷2=0 R1. Reading bottom to top: 101101.

Concept Tested: Decimal to Binary Conversion

7. In BCD (Binary-Coded Decimal), how is the decimal number 59 represented?

  1. 00111011
  2. 0101 1001
  3. 111011
  4. 0011 1011
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The correct answer is B. In BCD, each decimal digit is encoded separately using 4 bits. Decimal 5 = 0101 and decimal 9 = 1001, so 59 in BCD is 0101 1001. BCD is not a direct binary conversion—it encodes each digit independently.

Concept Tested: BCD Encoding

8. What condition indicates overflow in signed binary addition?

  1. The result has more bits than the operands
  2. The carry out of the MSB is 1
  3. Two positive numbers produce a negative result (or vice versa)
  4. The sum equals zero
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The correct answer is C. Overflow in signed addition occurs when the sign of the result is incorrect—specifically, when adding two positive numbers yields a negative result, or adding two negative numbers yields a positive result. This happens when the result exceeds the representable range.

Concept Tested: Overflow Detection

9. What is the hexadecimal equivalent of binary 11010110?

  1. D6
  2. B6
  3. 6D
  4. DA
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The correct answer is A. To convert binary to hex, group bits into sets of 4 from the right: 1101 0110. Then convert each group: 1101 = D (13), 0110 = 6. So 11010110 binary = D6 hexadecimal.

Concept Tested: Hex to Binary Conversion

10. Which statement correctly describes the relationship between octal and binary?

  1. Each octal digit represents 2 binary bits
  2. Each octal digit represents 3 binary bits
  3. Each octal digit represents 4 binary bits
  4. Octal and binary have no direct relationship
Show Answer

The correct answer is B. Octal is base 8, and since 8 = 2³, each octal digit represents exactly 3 binary bits. For example, octal 7 = binary 111, octal 5 = binary 101. This makes conversion between octal and binary straightforward by grouping bits in threes.

Concept Tested: Octal Numbers