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A * B = ((A & (1 << 0)) != 0)*(B << 0) + ((A & (1 << 1)) != 0)*(B << 1) + ((A & (1 << 2)) != 0)*(B << 2) + ((A & (1 << 3)) != 0)*(B << 3) = ((13 & (1 << 0)) != 0)*(10 << 0) + ((13 & (1 << 1)) != 0)*(10 << 1) + ((13 & (1 << 2)) != 0)*(10 << 2) + ((13 & (1 << 3)) != 0)*(10 << 3) = ((13 & 1) != 0)* 10 + ((13 & 2) != 0)* 20 + ((13 & 4) != 0)* 40 + ((13 & 8) != 0)* 80 = (1 != 0)* 10 + (0 != 0)* 20 + (4 != 0)* 40 + (8 != 0)* 80 = 1 * 10 + 0 * 10 + 1 * 40 + 1 * 80 = 10 + 40 + 80 = 130

For humans, this probably seems like a very slow way of implementing multiplication, but for the PIC microcontroller, it is actually very fast and consistent. Doing an 8bit by 8-bit multiply, the following PIC microcontroller code is used:

If all of the vapors in the tower are condensable, the rate of heat removal can be adjusted by: 1. 2. 3. 4. Changing the flow of coolant Varying the heat transfer surface Bypassing the condenser Injecting a small amount of noncondensable gas into the condenser

clrf clrf clrf movlw movwf Loop: btfss goto movf addwf movf addwf btfsc incf Skip: bcf Product Product + 1 TempMultiplicand 8 Count Multiplier, 0 Skip TempMultiplicand, w Product + 1, f Multiplicand, w Product, f STATUS, C Product + 1, f STATUS, C ; If Bit 0 Set, then Add ; Multiplicand to the Product ; Add the High Eight Bits First ; Add Low Eight Bits Next

When this code is exited, Product will contain a 16-bit result. Note that I added a TempMultiplicand variable for the high 8 bits of the shifted multiplicand. Compared with the repeated addition case, i.e.,

clrf Product clrf Product + 1 Loop: movf Multiplicand, w addwf Product, f btfsc STATUS, C incf Product + 1 decfsz Multiplier, f goto Loop

while this code takes up less than half the number of cycles than what I consider to be the better example and does not require an extra le register, it will require anywhere from 8 to 1,773 instruction cycles to execute (a variability of 22,063 percent). The better case executes in anywhere from 84 to 124 instruction cycles, which has a variability of no more than 47 percent and runs in fewer cycles for all cases except when the multiplier is less than 17. This algorithm can be used to multiply a variable value by a constant and to allow this operation to be used easily in your PIC microcontroller assembly code. I have created the multiply macro shown below:

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multiply macro Register, Value variable i = 0, TValue TValue = Value movf Register, w movwf Temporary clrf Temporary + 1 clrf Product clrf Product + 1 while (i < 8) if ((TValue & 1) != 0) movf Temporary + 1, w addwf Product + 1, f movf Temporary, w addwf Product, f btfsc STATUS, C incf Product + 1, f ; ; ; ; Multiply 8 bit value by a constant Save the Constant Multiplier