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I am trying to learn Binary Multiplication, 2's complement negative numbers.

-10 x 3

I know there is a simple way of doing this. Like sign extension and initial partial product.

-10 0110 twos complement x 3 x 0011 ---- ------ 000000 (initial partial product) with sign extension at the MSB 10110 (bit 0 of the 3 times 10, sign extended at MSB) 110110 (sign extended sum of initial partial product and Multiplicand) 10110- (bit 1 of the 3 multiplied by the 10. sign extension at the MSB Note the Multiplicand is shifted left by one bit)

I am lost on how to continue. I am not even sure if i was completely right up to this point. Can someone show me how to do it by steps? I dont want to do it any other way. If i do it the traditional way big numbers could be bad. Thank you

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Your interpretation of -10 is off.

 ..11110110 (-10) × 00000011 (3) ------------- ..11110110 (-10) + ..111101100 (-20) ------------- ..11100010 (-30)
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To clarify: you can't represent -10 in twos complement in only 4 bits: a 4 bit, 2s-complement integer runs from -8 to +7. So you must do your math with at least 5 bit integers and use at least 10 bits for representing the product.
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Hope This will help you. Use 2's complement. Overflows are discarded.

-10 in 2's complement is 0110. Add 1111 in front to make it 8 bits.

 11110110 (-10) 00000011 (3) ----------- 11110110 11110110 ----------- 1011100010 (discard [10])

answer = 11100010

when converted back, it's 30. that means the number represented by,11100010 is -30. (2's comp.)

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