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2's Complement Multiply with Constant

Discussion in 'Electronic Basics' started by Davy, Dec 14, 2005.

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  1. Davy

    Davy Guest

    Hi all,

    I have 2's Complement digit range from negtive to positive. How to
    multiply it with a constant?

    Now, I have to turn 2's complement to signed-digit format and do

    And there is a big problem confused me a long time:
    Is there any method have the merits from signed-digit(easy to multiply)
    and 2's complement(easy to add)?

    Any suggestions will be appreciated!
    Best regards,
  2. Ken Smith

    Ken Smith Guest

    Imagine a 16 bit 2's compliment number. The LSB has a value of 1, the
    next is 2 ... etc ... 16384. The top bit has a value of -32768.
  3. Guest

    I'm assuming doing this on platforms without a hardware multiplier or a
    multiply instruction. Otherwise multiplying with a constant is the same
    as multiplying with a variable.

    In which case, I don't get it. 2's complement is as easy to multiply as
    it is to add. There's no need to convert it to signed digit first.

    Lets look at some examples of 2's complement multiplication of negative
    numbers, we'll stick to 8 bits to make it short:

    -1 * 2 = -2
    11111111 (-1, shift left by 1 to multiply by 2)
    11111110 (equals -2)

    -5 * 4 = -20
    11111011 (-5 shift left by 2 to multiply by 4)
    11101100 (equals -20)

    -3 * 5 = -15
    11111101 (-3 shift left by 2 to multiply by 4)
    11110100 (equals -12 add -3)
    11110001 (equals -15)

    In none of the examples above do I need to convert to signed digit. If
    multiplying by a negative constant, then simply use the positive
    version of the constant and 2's complement the variable before
    multiplying (in effect multiplying it by -1):

    1 * -2 = -2
    00000001 (1, 2's complement to multiply by -1)
    11111111 (-1, shift left to multiply by 2)
    11111110 (equals -2)

    -1 * -2 = 2
    11111111 (-1, 2's complement to multiply by -1)
    00000001 (1, shift left to multiply by 2)
    00000010 (equals 2)

    I don't get what you're complaining about.
  4. Fixed-width 2's complement multiplication is the same as fixed-width
    unsigned multiplication. Just pretend you're doing unsigned multiplication;
    it'll work even if the value is negative.

    (This does not apply if you want a result larger than the operands, though.)

    -- Ben
  5. RED

    RED Guest

    Well you can do the sign extension of this "signed number" by the
    number of bits of the constant and then simple multiply.. i am assuming
    the constant to be a positive number. You can use the concept of adding
    the signed numbers (thats easy in 2's compliment) for multiplication...
    See the cases of overflow and avoid it..
  6. And of course if you do want the double size product, just remember
    that the 2-s compliment number is the same as (-2^n)+unsignedNum, so
    you can just subtract the other number in the upper half of the

    That is, if you have an unsigned product A*B=[C:D] with A, B, C and D
    all n bits long, if A is signed and B is not, the product is [C-B:D]
    and if both are signed, then it is [C-A-B:D].

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