EXASUB

  • Subtraction using 2’s complement method

    S.N0.DecimalSign MagnitudeOne ComplementTwo Complement
    00000000000000
    11000100010001
    22001000100010
    33001100110011
    44010001000100
    55010101010101
    66011001100110
    77011101110111
    8-010001111=(0000)’+1
    =1111 + 1
    =0000(discard MSB)
    9-110011110=(0001)’ + 1
    =(1110) + 1
    =1111
    10-210101101 =(0010)’ + 1
    =(1101) + 1
    =1110
    11-310111100 =(0011)’ + 1
    =(1100) + 1
    =1101
    12-411001011 =(0100)’ + 1
    =(1011) + 1
    =1100
    13-511011010 =(0101)’ + 1
    =(1010) + 1
    =1011
    14-611101001 =(0110)’ + 1
    =(1001) + 1
    =1010
    15-711111000 =(0111)’ + 1
    =(1000) + 1
    =1001
    16-8(not allowed in 4-bit) (not allowed in 4-bit) =(1000)’+1
    =(0111)+1
    =1000
    Table showing Decimal Numbers representation in sign-magnitude, one complement and two complement

    Subtraction using 2’s complement method is performed in microcontroller processors.

    To perform subtraction using 2’s complement method we need to do the following steps.

    step 1: Find the 2’s complement of subtrahend number.

    step 2: Add the 2’s complement of subtrahend to the minuend.

    step 3: Check the result for the carry.

    If there is carry generated.
    Then the result obtained is positive. And there is no further processing needed.

    If there is no carry generated.
    Then the result obtained is negative. And you have to do 2’s complement of the result obtained.

    NOTE:
    When doing subtraction using 2’s complement. Pay close attention to the sign of the subtrahend and minuend and the result.

    EXAMPLE:

    Ques.) 5 – 2 = ?
    Ans.) 5 – 2 = 3 (in decimal)

    using 2’s complement method
    (-2) representation in two’s complement form = 1110

    (5) in 2’s complement number = 0101

    0101
    + 1110
    ——-
    1 0011 = 3 (by discarding the MSB 1, Here MSB is the carry)
    There is a carry generated. So, the number is positive and no further processing is required.
    We can discard the carry.

    Ques.) -8 – 2 = ? in a 4-bit system
    Ans.) -8 – 2 = -10 (in decimal)
    Remeberwe have only 4 bit to store the number.
    using 2’s complement method
    (-2) representation in two’s complement form = 1110

    (-8) in 2’s complement number = 1000

    1000
    + 1110
    ——-
    1 0110 = 6 (by discarding the MSB 1, Here MSB is the carry)
    There is a carry generated. So, the number is positive and no further processing is required.
    But, the result obtained is wrong. Because if we add two numbers of the same sign result must be of the same sign. This condition creates an overflow.

    Overflow in 2’complement subtraction

    When two numbers of the same sign are added together and they produce a result with an opposite sign; An overflow has occurred and the result is not valid.

  • Convert Negative Decimal Number to Signed Binary number

    I have explained how negative signed decimal numbers are converted into binary equivalent.

  • Subtraction using 1’s complement method

    In this video, you will see the subtraction of two numbers using the one complement method. This one has a method in which the result contains an overflow bit. If after adding there is no overflow carry. Then the result is negative and you have to complement it again.

  • Unsigned and Signed Number

  • How Integer and Floating point numbers are stored in computers

    The number has two parts.

    1. Integer Part
    2. Fraction Part

    Integers are numbers without the fraction part.
    They can range from negative infinity to positive infinity.
    Integers are further divided into two parts.

    1. Unsigned number (0 to (2^n – 1); here n = width of data bus)
    2. Signed Numbers ((-2^(n-1)) to (2^n – 1))

    Fractional numbers or Floating Point numbers are stored in a standard format known as IEEE 754.
    IEEE 754 Floating-Point Standard comes in three different modes.

    1. Single precision Format (32 bits)
    2. Double-precision format


  • Convert Hexadecimal number to Octal Number

    Convert the number into its binary equivalence first and the make group of three digits starting from LSB and moving towards the MSB. Then you have to write the just convert the group into an octal number which will easy.

  • Why does zero divided by zero tends to infinity?

  • Hexadecimal Number System

    In this video, I have told about the hexadecimal number system. The hexadecimal number system is widely used in electronic computer systems to represent the number systems. I have also described that we can represent fractions in the hexadecimal number system also.

  • Octal Number System

    In the octal Number system, we start counting from 0 which goes up to 7. Making only 8 digits. Then after 7, we start by incrementing 1 to the tenth place and start counting from 0 up to 17.

    In the video, I have described what the octal number system is and how we can convert the octal number to decimal numbers.

    Just like we have fractions in decimals like 1.234, 3.9864 etc. we also have fractions in the octal number system as well like 7741.2225, 12345.654 etc.

  • Binary Number System

    In a binary number system, there are only two possible states, HIGH state and LOW state.
    These two states can be represented by current levels, voltage levels, bumps and valleys on the surface of CD/DVD etc.

    The two states are generally represented by a ‘0’ for LOW state and by a ‘1’ for the HIGH state.

    Using the combination of 0’s(LOW) and 1’s(HIGH), we can represent the other number systems such as hexadecimal, octal or decimal into
    binary number system.

    Bit Nibble Byte Word Dword Qword

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