Computer Science Fundamentals - Discrete Math Part 1
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Questions and Answers

What is the final true value of the octal number 21772?

  • 9210
  • 921010 (correct)
  • 91020
  • 9120

    • Radix conversion only involves changing binary numbers into decimal numbers.

    False

    What is the base of the hexadecimal number system?

    16

    The octal number system is also known as base ____.

    <p>8</p> Signup and view all the answers

    How is the final value of a binary number calculated?

    <p>By adding the weights of each digit that is 1.</p> Signup and view all the answers

    Match the numeral system with its radix:

    <p>Octal = 8 Hexadecimal = 16 Decimal = 10 Binary = 2</p> Signup and view all the answers

    What is the weight of the first digit from the right in the octal number 21772?

    <p>1</p> Signup and view all the answers

    The weight of a digit in any numeral system is determined by its position.

    <p>True</p> Signup and view all the answers

    What is the result of the hexadecimal addition 1B16 + F16?

    <p>2A16</p> Signup and view all the answers

    The hexadecimal number system uses a base of 16.

    <p>True</p> Signup and view all the answers

    What is the decimal result of the binary addition 110112 + 11112?

    <p>1010102</p> Signup and view all the answers

    The octal number system uses a base of _____.

    <p>8</p> Signup and view all the answers

    What is the decimal result of 628 – 268?

    <p>348</p> Signup and view all the answers

    Match the following operations with their results.

    <p>2710 + 1510 = 4210 338 + 178 = 528 5010 – 2210 = 2810 3216 - 1616 = 1C16</p> Signup and view all the answers

    In hexadecimal multiplication, if the quotient is 3, after carrying over, the next operand becomes _____ before division.

    <p>38</p> Signup and view all the answers

    What is the result of the octal operation 1100102 - 101102?

    <p>111002</p> Signup and view all the answers

    What is the correct binary representation of the decimal number 156?

    <p>10011100</p> Signup and view all the answers

    The fractional part of a decimal can be converted to binary by dividing by 2 until the result becomes 0.

    <p>False</p> Signup and view all the answers

    What is the greatest power of 2 that fits into 156?

    <p>128</p> Signup and view all the answers

    To convert the integer part to binary, repeatedly divide by 2 until the quotient becomes _____ .

    <p>0</p> Signup and view all the answers

    Match the following steps with their corresponding descriptions:

    <p>1 = Choosing the greatest power of 2 2 = Subtracting to get the new dividend 3 = Writing down binary digits 4 = Listing powers of 2</p> Signup and view all the answers

    Which of the following describes the process of converting the fractional part of a decimal to binary?

    <p>Multiply by 2 until 0</p> Signup and view all the answers

    What is the final true value of the decimal number 21998?

    <p>2199810</p> Signup and view all the answers

    What sequence of operations do you perform to convert the integer part to binary?

    <p>Divide by 2 and note the remainders.</p> Signup and view all the answers

    Hexadecimal numbers use the digits from 0 to 9 and include letters A to F.

    <p>True</p> Signup and view all the answers

    When converting a decimal number to binary, you write down '0' for each power of 2 that cannot fit into the current dividend.

    <p>True</p> Signup and view all the answers

    What is the base (radix) of octal numbers?

    <p>8</p> Signup and view all the answers

    To convert a hexadecimal number to decimal, each digit is multiplied by the weight of the radix (______)

    <p>16</p> Signup and view all the answers

    What is the value of the binary number 11001 in decimal?

    <p>25</p> Signup and view all the answers

    In octal numbers, the exponent for the fractional part starts from -1.

    <p>True</p> Signup and view all the answers

    What digits do octal numbers use?

    <p>0 to 7</p> Signup and view all the answers

    Match the following number systems with their bases:

    <p>Decimal = 10 Binary = 2 Octal = 8 Hexadecimal = 16</p> Signup and view all the answers

    What is the minimum unit that represents a binary state in computers?

    <p>Bit</p> Signup and view all the answers

    In computers, a byte consists of 16 bits.

    <p>False</p> Signup and view all the answers

    How many different states can be represented with 3 bits?

    <p>8</p> Signup and view all the answers

    The unit of processing inside computers that consists of multiple bits is called a _____

    <p>word</p> Signup and view all the answers

    Match the following data units with their respective sizes:

    <p>Bit = 1 bit Byte = 8 bits Word (32 bit) = 32 bits Word (64 bit) = 64 bits</p> Signup and view all the answers

    Which of the following statements about bits and bytes is true?

    <p>Bits are used to create larger data units such as bytes.</p> Signup and view all the answers

    The information amount that can be represented with 2 bits is 2 types.

    <p>False</p> Signup and view all the answers

    What are two states represented by electric signals in data representation?

    <p>0 and 1</p> Signup and view all the answers

    What is the first step in converting an n-adic number into a decimal number?

    <p>Multiply each digit by the weight of its position</p> Signup and view all the answers

    When converting a decimal number to an n-adic number, the fractional part is handled by dividing by n repeatedly.

    <p>False</p> Signup and view all the answers

    What procedure is used to convert the integer part of a decimal number into an n-adic number?

    <p>Repeatedly divide by n until the quotient is 0, and arrange the remainders.</p> Signup and view all the answers

    When converting a decimal number like (0.2)10 to binary, the result may lead to a ______.

    <p>recurring fraction</p> Signup and view all the answers

    Match the following processes with their correct descriptions:

    <p>Conversion of integer part = Divide by n and track remainders Conversion of fractional part = Multiply by n until it becomes 0 Binary to octal conversion = Group binary digits in sets of three Binary to hexadecimal conversion = Group binary digits in sets of four</p> Signup and view all the answers

    Why is it sometimes easier to convert from decimal to binary before converting to octal or hexadecimal?

    <p>Binary can be converted directly to n-adic bases</p> Signup and view all the answers

    The result of converting a fractional number that has no finite representation is treated as an exact value in computations.

    <p>False</p> Signup and view all the answers

    What happens when applying radix conversion to a decimal number that gets into a loop?

    <p>It is treated as an approximate value.</p> Signup and view all the answers

    Study Notes

    Computer Science Fundamentals - Basic Theory on Discrete Mathematics (Part 1)

    • Objectives:
      • Understand how computers represent numerical values, including base systems (radix), converting between bases, and arithmetic operations.
      • Understand the rules and techniques for sets, logical operations, and Karnaugh maps.

    Data Representation in Computers

    • Unit of Representation: Computers store data as electrical signals represented by two states: current flowing (high voltage) or not flowing (low voltage).
    • Bit: The smallest unit of data in computers, representing 0 or 1.
    • Byte: A collection of 8 bits, forming a larger unit of data.
    • Word: A collection of bits larger than a byte (e.g., 16 bits, 32 bits, 64 bits). Longer words allow for faster processing of larger amounts of data.

    Information Amount

    • The number of possible combinations of 0s and 1s determines the amount of information.
    • n bits can represent 2n possible values.
      • 1 bit = 2 values
      • 2 bits = 4 values
      • 8 bits (1 byte) = 256 values
      • 16 bits (1 word) = 65,536 values

    Radix Systems

    • Radix (base) is the number of digits used in a numerical system.
    • Common radix systems include:
      • Decimal (base 10)
      • Binary (base 2)
      • Octal (base 8)
      • Hexadecimal (base 16)
    • Prefixes are used to represent very large or very small numbers (e.g., Kilo (k) = 103, Mega(M) = 106, etc.)
      • Note that these values in computer science often correspond or are close to 2x values.

    Radix Conversion

    • Converting between different radix systems (e.g., binary to decimal, decimal to hexadecimal)
      • Integer parts converted through division and remainders
      • Fractional parts using multiplication.
      • These processes handle the conversion of integers and fractional parts individually.

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    Computer Science Fundamentals - Basic Theory on Discrete Mathematics (Part 1) PDF

    Description

    This quiz covers basic theories in discrete mathematics relevant to computer science. It explores data representation, including number systems, bits, bytes, and the fundamental principles of logical operations. Understanding sets and Karnaugh maps will also be examined.

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