Number Systems and Conversions Quiz

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Questions and Answers

What is the equivalent of decimal 15 in hexadecimal?

  • C
  • E
  • D
  • F (correct)

Which number is represented as '1010' in decimal?

  • 14
  • 12
  • 8
  • 10 (correct)

In which number system is the symbol '1' used exclusively?

  • Decimal
  • Octal
  • Binary (correct)
  • Hexadecimal

Which of the following numbers is represented as '1101' in decimal?

<p>13 (A)</p>
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What is the base of the hexadecimal number system?

<p>16 (C)</p>
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What is the binary representation of the octal number 7058?

<p>1110001012 (D)</p>
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How would you convert the decimal number 123410 to octal?

<p>Divide by 8 and use the remainders. (B)</p>
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What is the binary representation for the hexadecimal number 10AF16?

<p>00010000101011112 (B)</p>
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To convert from binary to octal, how do you group the bits?

<p>In groups of three from right to left. (A)</p>
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Which of the following correctly converts the binary number 10101110112 to hexadecimal?

<p>2BB16 (A)</p>
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What is the output when converting the decimal number 123410 to hexadecimal?

<p>4D216 (C)</p>
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How would you convert an octal number directly to hexadecimal?

<p>Use binary as an intermediary. (A)</p>
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When converting the hexadecimal number 1F0C16 to octal, which method is used?

<p>Use binary as an intermediary. (B)</p>
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What is the decimal equivalent of the binary number 101011?

<p>43 (B)</p>
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How do you convert the octal number 724 to decimal?

<p>7 x 8^2 + 2 x 8^1 + 4 x 8^0 (B)</p>
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What is the first step in converting a decimal number to binary?

<p>Divide by two and track remainders (B)</p>
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What is the hexadecimal equivalent of the decimal number 2748?

<p>ABC (D)</p>
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Which of the following correctly describes the position of the bits when converting binary to decimal?

<p>The bit position starts from 0 on the right (D)</p>
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To convert the hexadecimal number ABC to decimal, which calculations should be performed?

<p>C x 16^0 + B x 16^1 + A x 16^2 (B)</p>
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What method is used when converting octal numbers to decimal?

<p>Multiply each digit by 8^n (D)</p>
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When converting a binary number like 1100 to decimal, which bit contributes to the highest value?

<p>The leftmost bit (C)</p>
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What is the decimal equivalent of the binary number '1110101'?

<p>117 (B)</p>
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In computing, what is the value of the prefix 'M' in base 2?

<p>1048576 (A)</p>
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Which of the following correctly lists the decimal equivalent of the hexadecimal number '1AF'?

<p>703 (B)</p>
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What is the result of adding the binary numbers '10101' and '11001'?

<p>101110 (A)</p>
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What is the equivalent octal representation of the decimal number 33?

<p>41 (A)</p>
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What does the prefix 'p' represent in the metric system?

<p>0.000000000001 (D)</p>
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Which of the following is the correct binary representation of the decimal number 75?

<p>1001011 (A), 1001011 (C)</p>
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In the context of common powers, what is 10^6 commonly known as?

<p>mega (C)</p>
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Flashcards

Decimal Number System

A number system with base 10, using the symbols 0-9.

Binary Number System

A number system with base 2, using the symbols 0 and 1.

Octal Number System

A number system with base 8, using the symbols 0-7.

Hexadecimal Number System

A number system with base 16, using the symbols 0-9 and A-F.

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Decimal to Binary Conversion

Repeated division by 2, noting the remainders, which are then read in reverse order.

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Binary to Decimal Conversion

Multiply each bit by 2^n, where n is the bit position (from right starting at 0).

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Decimal to Octal Conversion

Repeated division by 8, tracking the remainders.

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Octal to Decimal Conversion

Multiply each digit by 8^n, where n is the digit's position (from right starting at 0).

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Decimal to Hexadecimal Conversion

Repeated division by 16, noting the remainders (0-9, A-F).

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Hexadecimal to Decimal Conversion

Multiply each digit by 16^n, where n is the digit's position (from right starting at 0).

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Binary to Octal Conversion

Group binary digits into sets of three (starting from the right) and convert each group to its octal equivalent.

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Binary to Hexadecimal Conversion

Group binary digits into sets of four (starting from the right) and convert each group to its hexadecimal equivalent.

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Octal to Binary Conversion

Convert each octal digit to its 3-bit binary representation.

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Hexadecimal to Binary Conversion

Convert each hexadecimal digit to its 4-bit binary representation.

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Hexadecimal to Octal Conversion

Convert to binary first, then group the binary into threes and convert to octal.

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Octal to Hexadecimal Conversion

Convert to binary first, then group the binary into fours and convert to hexadecimal.

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pico (p)

10^(-12)

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nano (n)

10^(-9)

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micro (µ)

10^(-6)

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milli (m)

10^(-3)

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kilo (k)

10^(3)

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mega (M)

10^(6)

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giga (G)

10^(9)

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tera (T)

10^(12)

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kilo (k) in Base 2

2^10 = 1024

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mega (M) in Base 2

2^20 = 1,048,576

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giga (G) in Base 2

2^30 = 1,073,741,824

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Binary 1-Bit Addition

Basic rules for adding single bits in binary.

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Binary n-Bit Addition

Add bits column by column, carrying over when the sum is 2 or more.

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Study Notes

Number Systems

  • Common number systems: decimal, binary, octal, hexadecimal
  • Decimal: base 10, uses symbols 0-9
  • Binary: base 2, uses symbols 0 and 1, used in computers
  • Octal: base 8, uses symbols 0-7
  • Hexadecimal: base 16, uses symbols 0-9 and A-F

Quantities and Counting

  • Numbers can be represented in different number systems
  • Example: The decimal number 10 is equal to 1010 in binary, 12 in octal and A in hexadecimal

Conversion Between Number Systems

  • Decimal to Decimal: Just for fun, no conversion needed
  • Decimal to Binary: Divide by 2 repeatedly, keep track of remainders
  • Decimal to Octal: Divide by 8 repeatedly, keep track of remainders
  • Decimal to Hexadecimal: Divide by 16 repeatedly, keep track of remainders
  • Binary to Decimal: Multiply each bit by 2^n, where n is the bit position starting from 0 on the right
  • Octal to Decimal: Multiply each bit by 8^n, where n is the bit position starting from 0 on the right
  • Hexadecimal to Decimal: Multiply each bit by 16^n, where n is the bit position starting from 0 on the right
  • Binary to Octal: Group bits in threes, starting from the right, convert to octal digits
  • Binary to Hexadecimal: Group bits in fours, starting from the right, convert to hexadecimal digits
  • Octal to Binary: Convert each octal digit to a 3-bit binary representation
  • Hexadecimal to Binary: Convert each hexadecimal digit to a 4-bit binary representation
  • Octal to Hexadecimal: Use binary as an intermediary
  • Hexadecimal to Octal: Use binary as an intermediary

Common Powers

  • Base 10:
    • pico (p) = 10^-12
    • nano (n) = 10^-9
    • micro (µ) = 10^-6
    • milli (m) = 10^-3
    • kilo (k) = 10^3
    • mega (M) = 10^6
    • giga (G) = 10^9
    • tera (T) = 10^12
  • Base 2: (used in computing, particularly for memory)
    • kilo (k) = 2^10 = 1024
    • mega (M) = 2^20 = 1,048,576
    • giga (G) = 2^30 = 1,073,741,824

Binary Addition

  • Adding two 1-bit values:
    • 0 + 0 = 0
    • 0 + 1 = 1
    • 1 + 0 = 1
    • 1 + 1 = 10 (carry over the "1")
  • Adding two n-bit values:
    • Add individual bits
    • Propagate carries

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