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Karatsuba multiplication of az+b and cz+d (boxed), and 1234 and 567 with z=100. Magenta arrows denote multiplication, amber denotes addition, silver denotes subtraction and cyan denotes left shift. (A), (B) and (C) show recursion with z=10 to obtain intermediate values. The Karatsuba algorithm is a fast multiplication algorithm.
On currently available processors, a bit-wise shift instruction is usually (but not always) faster than a multiply instruction and can be used to multiply (shift left) and divide (shift right) by powers of two. Multiplication by a constant and division by a constant can be implemented using a sequence of shifts and adds or subtracts. For ...
During the addition, each carry is "signaled" rather than performed, and during the carry cycle, the machine increments the digits above the "triggered" digits. This operation has to be performed sequentially, starting with the ones digit, then the tens, the hundreds, and so on, since adding the carry can generate a new carry in the next digit.
A partially disassembled Curta calculator, showing the digit slides and the stepped drum behind them Curta Type I calculator, top view Curta Type I calculator, bottom view. The Curta is a hand-held mechanical calculator designed by Curt Herzstark. [1] It is known for its extremely compact design: a small cylinder that fits in the palm of the hand.
4 − 5 × 6: The multiplication must be done first, and the formula has to be rearranged and calculated as −5 × 6 + 4. So ± and addition have to be used rather than subtraction. When + is pressed, the multiplication is performed. 4 × (5 + 6): The
P = 1110 1001 1. Arithmetic right shift. P = 1110 1001 1. The last two bits are 11. P = 1111 0100 1. Arithmetic right shift. The product is 1111 0100, which is −12. The above-mentioned technique is inadequate when the multiplicand is the most negative number that can be represented (e.g. if the multiplicand has 4 bits then this value is −8 ...
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The 2 on the top scale is placed over the 5.5 on the bottom scale. The resulting quotient, 2.75 , can then be read below the top scale's 1 : There is more than one method for doing division, and the method presented here has the advantage that the final result cannot be off-scale, because one has a choice of using the 1 at either end.