Binary Addition Rules and Number Representation Quiz
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Questions and Answers

What is a common symbol used in binary representation?

  • 2 (correct)
  • 3
  • 7
  • 5
  • When adding in binary, what happens if you run out of digits?

  • You add another bit to continue the addition
  • You carry over the remaining digit to the final answer (correct)
  • You add a 1 to the rightmost bit and continue
  • You ignore the carry and stop adding
  • In binary addition, what is done when the sum exceeds two digits?

  • The sum is discarded
  • The sum is truncated to fit in a single digit
  • A carry is generated to the next bit position (correct)
  • The sum is divided by 2
  • What is the binary representation of the decimal number 10?

    <p>1010</p> Signup and view all the answers

    In binary addition, what does it mean to 'Add with Carry'?

    <p>Consider any carry from the previous addition</p> Signup and view all the answers

    When adding two binary numbers, what do we do if the sum is greater than 1 for a single bit?

    <p>Generate a carry to the next higher bit</p> Signup and view all the answers

    What is the main difference between binary and decimal number systems?

    <p>Binary system uses digits from 0 to 1, while decimal system uses digits from 0 to 9</p> Signup and view all the answers

    Why is it necessary to have carry digits in binary addition?

    <p>To indicate that the sum is greater than the highest single digit in binary</p> Signup and view all the answers

    What happens when you compute 1 + 1 in binary?

    <p>A carry of 1 is needed</p> Signup and view all the answers

    Why do we represent the result of 10 as two separate digits in binary addition?

    <p>Because it exceeds the limit of single binary digit</p> Signup and view all the answers

    What does the highest digit in binary represent?

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

    Why do we need to be careful with carrying and borrowing in binary addition and subtraction?

    <p>To avoid errors due to running out of available digits while adding or subtracting</p> Signup and view all the answers

    What is the result of 25 - 123 using 8-bit 2’s complement?

    <p>01100001</p> Signup and view all the answers

    What is the 1's complement of the subtrahend in the subtraction example provided?

    <p>10000100</p> Signup and view all the answers

    Which rule of binary addition states '0 - 1 = 1 (borrow 1 from the more significant bit)'?

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

    What does 'No carry implies negative number' mean in binary arithmetic?

    <p>The result is negative</p> Signup and view all the answers

    How do we obtain the value after performing a binary subtraction when there is no carry?

    <p>Performing a 2's complement of the result</p> Signup and view all the answers

    What is the rule of binary multiplication stating '1 x 1 = 1 (no carry or borrow bits)'?

    <p>'1x1=1'</p> Signup and view all the answers

    Study Notes

    Binary Representation

    • Non-negative integers are represented in Binary with Most Significant Bit (MSB) and Least Significant Bit (LSB)
    • Binary representation uses only 2 symbols: 0 and 1

    Binary Addition

    • Binary addition is similar to decimal addition, but with 2 digits only (0 and 1)
    • Carry and borrow rules apply, with careful handling of digits
    • Example: 5 + 7 in binary form (1012 + 1112) with carry and borrow

    Binary Subtraction

    • Binary subtraction is similar to decimal subtraction
    • Example: 25 - 123 using 8-bit 2's complement representation

    Binary Arithmetic Rules

    • Rules of Binary Addition:
      • 0 + 0 = 0
      • 0 + 1 = 1
      • 1 + 0 = 1
      • 1 + 1 = 0 (carry 1 to the next more significant bit)
    • Rules of Binary Subtraction:
      • 0 - 0 = 0
      • 0 - 1 = 1 (borrow 1 from more significant bit)
      • 1 - 0 = 1
      • 1 - 1 = 0
    • Rules of Binary Multiplication:
      • 0 × 0 = 0
      • 0 × 1 = 0
      • 1 × 0 = 0
      • 1 × 1 = 1 (no carry or borrow bits)

    Binary Multiplication

    • Binary multiplication follows the same process as decimal multiplication
    • Multiply each digit of the second number by the first whole number, then add them, shifting each resulting multiplication one digit to the left.

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    Description

    Test your knowledge on binary addition rules and number representation. Learn how to add binary numbers and how to deal with carrying over digits in multi-digit additions.

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