Ignore the decimal places and complete the multiplication as if operating on two integers. There's 3 total decimal places in both numbers. Insert a decimal point in the product so it has the same number of decimal places equal to the total from step 1.Įxample Long Multiplication with Decimals.Multiply the numbers using long multiplication. ![]() It features a syntax-highlighted scrollable display and is designed to be fully used via keyboard. Ignore the decimals and right align the numbers one on top of the other as if they were integers SpeedCrunch is a high-precision scientific desktop calculator.Count the total number of decimal places contained in both the multiplicand and the multiplier.Long multiplication with decimals using the standard algorithm has a few simple additional rules to follow. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.When you finish multiplying, draw another answer line below your last row of answer numbers. ![]() Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.If you carried a digit, add it to the result and write the answer below the equals line. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If that answer is greater than nine, write the ones place as the answer and carry the tens digit.Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.The number with the most digits is usually placed on top as the multiplicand. Arrange the numbers one on top of the other and line up the place values in columns.These are the steps to do long multiplication by hand: The traditional method, or Standard Algorithm, involves multiplying numbers and lining up results according to place value. so you can't easily use non-widening imul if you want to detect when the full unsigned result didn't fit.Long multiplication means you're doing multiplication by hand. (Or if you want FLAGS set according to unsigned overflow of the low half, instead of signed overflow. SpeedCrunch is a high-precision scientific desktop calculator. There no concept of distribution explained. The only doc SpeedCrunch has is: According to the doc ab ab : multiplication. Only widening multiply needs a separate form. This is probably a hidden undocumented way of SpeedCrunch to favor distribution over multiplication and division but the programmed rule is not explicitly written in the doc. The low half of signed and unsigned multiply is the same, that's why x86 for example only has immediate and 2-operand forms of imul, not also mul. ![]() Widening signed-multiply doesn't involve any truncation. Or for another example, see Why are signed and unsigned multiplication different instructions on x86(-64)? ![]() But the full signed result is not always the operand-size truncation of the unsigned product.įor example, -128 * 127 is -16256, or as 16-bit 2's complement, 0xc080.īut 0x80 * 0x7f is + 16256, i.e. (249-256) * (243-256) = 0x005b, a small positive result that happens to fit in the low half of the full result. I think your choice of example misled you into thinking the signed product could be obtained by truncating the 8x8 => 16-bit unsigned product down to 8 bits.
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