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where Register is the le register containing the multiplicand to be multiplied with the multiplier in Constant. The result will be stored in the 16-bit variable Product. The macro itself will insert the code needed to perform the operation, but without the looping functions. This method of shifting data is how I perform all multiplication in the PIC microcontroller. If you look at Appendix G, you will see that this is the method used to multiply two 16-bit numbers together. Division is always much more dif cult to perform than multiplication. Since multiplication is repeated addition, division could be thought of as repeated subtraction. The basic code version for division is

Remainder = Dividend; for (Quotient = 0; (Dividend Divisor) > 0; Quotient++) Dividend = Dividend Divisor; Remainder = Remainder (Quotient * Divisor);

This code also includes returning a remainder from the operation. To simplify the division operation, I can use an arithmetic series like I did for multiplication, but this one will work differently than multiplication. I would call the series produced for multiplication a closed series because the series is de ned for a set range of numbers. In division, this is possible for some numbers, but not for all; numbers do not always divide evenly (i.e., have a remainder equal to zero) into others. In these cases, a decision has to be made about what to do about them. To come up with a division arithmetic series, I would want to use the property of division that a number can be divided by a second one by multiplying by the reciprocal of the second number. This can be shown as

A/B = A * (1/B)

Each of the above has certain advantages and disadvantages. Schemes (1) and (4) are perhaps the most common, but not necessarily the most effective. As seen in Chap. 9, the rate of cooling is quite insensitive to changes in coolant flow at the velocities under which most condensers are operated. This arrangement does conserve cooling water, however. An equal-percentage valve is recommended. Scheme (2) is very effective in the absence of noncondensable gases. Figure 11.10 shows how the heat transfer area can be changed by flooding the condenser tubes with liquid. The reflux flow essentially sets the separation factor for the tower. If vapor flow into the condenser exceeds liquid flow out, condensate will rise to cover more heat transfer surface. This will cause a pressure rise, which in turn will reduce the heat input through the pressure controller. Because of the rapid response of vapor flow to heat input, this is a fairly fast loop. Scheme (3), while effective, has the disadvantage of requiring an extremely large valve. Because the valve is in parallel with a fixed resistance (the condenser), a quick-opening characteristic is desirable. A butterfly valve is often used, however, because of its low pressure drop. Scheme (4) intentionallv introduces noncondensable gas into the condenser, ultimately reducing its heat transfer capability to that required by the heat input. But a path must be open for release of the gas in the

This probably will be unexpected because fractions (which are what reciprocals really are) are not possible in the PIC microcontroller; to get around this problem, you just have to look back in the history of mathematics to see how this problem has been encountered