Computer Science Fundamentals Quiz
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Questions and Answers

What is the complement of product equal to according to De-Morgans Law?

The sum of its complement

Boolean Laws are based on basic logic gates.

True

What is a gate's function in a digital circuit?

  • Produce analog output
  • Allow flow of digital information
  • Block flow of digital information
  • Both allow and block flow of digital information (correct)

    • The computer can understand only a few symbols called digits and these symbols describe different values depending on the position they hold in the number. In general, the ____ number system is used in computers.

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

    What is the process involved in performing 2's complement?

    <p>Take the 2's complement of both negative numbers and use regular binary addition.</p> Signup and view all the answers

    Codes are classified into how many types?

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

    Which of the following is an example of a weighted code?

    <p>Binary-coded Decimal (BCD)</p> Signup and view all the answers

    Gray code is a non-weighted code suitable for arithmetic operations.

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

    Which base has an allowed digit range of 0 to 9?

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

    In Hexadecimal, the allowed digits range from 0 to _?

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

    In Octal number system, the base is 10.

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

    Match the Number System Conversion representation column with the correct explanation column:

    <p>O-&gt;H = Octal to Hexadecimal H-&gt;O = Hexadecimal to Octal H-&gt;B = Hexadecimal to Binary O-&gt;B = Octal to Binary</p> Signup and view all the answers

    What is the technique to convert Binary to Decimal, starting from the 0 bit weight and adding the results?

    <p>Multiply each bit by the weight (2^n) and add the results</p> Signup and view all the answers

    Convert (.640625)10 to base 8.

    <p>(.51)8</p> Signup and view all the answers

    How can remainders be arranged for Decimal to Binary conversion?

    <p>Arrange the remainders from last to first</p> Signup and view all the answers

    Convert 123410 to base 16.

    <p>4D216</p> Signup and view all the answers

    What is the technique used in Decimal to Octal conversion for the whole number part?

    <p>Divide by 8, keep track of the remainders, and arrange them from last to first</p> Signup and view all the answers

    Convert (0.6295)10 to base 16.

    <p>(0.A126E)16</p> Signup and view all the answers

    Convert 10110101112 to base 8.

    <p>13278</p> Signup and view all the answers

    Convert 7058 to base 2.

    <p>1110001012</p> Signup and view all the answers

    Convert 10AF16 to base 2.

    <p>00010000101011112</p> Signup and view all the answers

    Convert 10101110112 to base 16.

    <p>2BB16</p> Signup and view all the answers

    Match the following number representation techniques with their descriptions:

    <p>Sign Magnitude = Representation using one bit for the sign and the rest for the magnitude 1’s Complement = Taking the complement of the binary number 2’s Complement = Taking the 1’s complement and adding 1</p> Signup and view all the answers

    The 2’s complement process can be used for both addition and multiplication.

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

    Study Notes

    Boolean Algebra and Logic Gates

    • The Boolean laws are based on the basic logic gates: AND, OR, and NOT.
    • There are 9 Boolean laws, including:
      • A + A = A
      • A + 0 = A
      • A + 1 = 1
      • A + A’ = 1
      • A.A = A
      • A.A’ = 0
      • A.1 = A
      • A.0 = 0
      • (A’)’ = A
    • De Morgan's Law has two statements:
      • The complement of the product is equal to the sum of the complements.
      • The complement of the sum is equal to the product of the complements.
    • De Morgan's Law can be proved using a truth table.
    • Digital logic gates are the basic building blocks of digital circuits.
    • There are three basic logic gates: AND, OR, and NOT.
    • Hybrid gates are derived from the basic logic gates.
    • NAND and NOR gates are universal gates.

    Number Systems

    • Computers understand only numbers, so letters and words are translated into numbers.
    • The binary number system is used in computers, but octal, decimal, and hexadecimal systems are also used.
    • Number systems have different bases, including:
      • Binary (base 2): 0 and 1
      • Octal (base 8): 0 to 7
      • Decimal (base 10): 0 to 9
      • Hexadecimal (base 16): 0 to 9 and A to F
    • Number systems can be converted from one to another using division and multiplication by the base of the target system.
    • Conversion techniques for decimal to binary and octal include:
      • Divide by the base of the target system and keep track of the remainder.
      • Multiply by the base of the target system and record the carry.
    • Examples of number system conversions include:
      • Binary to decimal: 11011011.1012 = 219.7510
      • Octal to decimal: 5728 = 37810
      • Hexadecimal to decimal: 3A9416 = 15996

    Conversion Techniques

    • Decimal to binary conversion involves:
      • Divide by 2 and keep track of the remainder.
      • Arrange the remainders in reverse order.
    • Decimal to binary conversion for fractions involves:
      • Multiply by 2 and record the carry.
      • Arrange the remainders in reverse order.
    • Decimal to octal conversion involves:
      • Divide by 8 and keep track of the remainder.
      • Arrange the remainders in reverse order.
    • Examples of decimal to binary conversions include:
      • 156410 = 11000011100
      • 0.65265 = 0.10101### Number Systems Conversion
    • Decimal to Hexadecimal conversion:
      • Technique: Divide by 16, keep track of remainders, arrange in reverse order
      • Example: (1234)10 = (4D2)16
    • Decimal to Hexadecimal conversion for fractions:
      • Technique: Multiply by 16, record carry, keep track of remainders, arrange in reverse order
      • Example: (0.6295)10 = (0.A126E)16
    • Binary to Octal conversion:
      • Technique: Group bits in threes, convert to octal digits
      • Example: (101101011)2 = (1327)8
    • Octal to Binary conversion:
      • Technique: Convert each octal digit to a 3-bit binary equivalent
      • Example: (705)8 = (111000101)2
    • Hexadecimal to Binary conversion:
      • Technique: Convert each hexadecimal digit to a 4-bit binary equivalent
      • Example: (10AF)16 = (0001000010101111)2
    • Binary to Hexadecimal conversion:
      • Technique: Group bits in fours, convert to hexadecimal digits
      • Example: (101011101)2 = (2BB)16
    • Octal to Hexadecimal conversion:
      • Technique: Use binary as an intermediary (O -> B -> H)
      • Example: (107)8 = (23E)16
    • Hexadecimal to Octal conversion:
      • Technique: Use binary as an intermediary (H -> B -> O)
      • Example: (1F0C)16 = (1741)8

    2's Complement Representation

    • Sign-Magnitude Representation:
      • Range: -2^(n-1) to 2^(n-1) - 1
      • Example: -17 = 110001 (n=8)
    • 1's Complement Representation:
      • Range: -2^(n-1) to 2^(n-1) - 1
      • Example: -17 = 10111011 (n=8)
    • 2's Complement Representation:
      • Range: -2^(n-1) to 2^(n-1) - 1
      • Example: -17 = 11101001 (n=8)

    2's Complement Arithmetic

    • Addition and Subtraction using 2's Complement:
      • Example: 5 + (-3) = 2, (-9) + 5 = 4
    • Overflow detection:
      • Check if carry-in and carry-out of MSB are different
    • 2's Complement Process:
      • Complement digits, add 1
      • Example: -5 = 11111011, 13 = 00001101

    Code Representation

    • Binary-Coded Decimal (BCD):
      • Weights: 8, 4, 2, 1
      • Example: (45)10 = (01000101)BCD
    • Excess-3 Code:
      • Represent decimal numbers as binary, adding 3 to each digit
      • Example: (4)10 = (011)E3
    • Gray Code:
      • Non-weighted code, used in input/output devices and analog-to-digital converters
      • Example: (4)10 = (110)GC

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    Test your knowledge of digital systems, Boolean algebra, and number systems, including logic gates, PLDs, and number conversions.

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