New PDF release: A treatise on differential equations

By George Boole

ISBN-10: 140218364X

ISBN-13: 9781402183645

This Elibron Classics ebook is a facsimile reprint of a 1877 version via Macmillan and Co., London.

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Example text

Compare. This instruction is useful for boundary, magnitude and equality checks. Most implementations perform a comparison by subtracting one value from another. This process affects neither operand, but sets the appropriate flags. Many microprocessors allow either signed or unsigned comparisons. Multiplication Multiply. This instruction performs a standard unsigned multiply based on the word size of the particular microprocessor or microcontroller. Hardware can make life easier. On the 8088 and 8086, this instruction was embarrassingly slow and not that much of a challenge to shift and add routines.

Carry. Whether this flag is set or reset after a certain operation varies from processor to processor. On the 8086, the carry will be set if an addition overflows or a subtraction underflows. On the 80C196, the carry will be set if that addition overflows but cleared if the subtraction underflows. Be careful with this one. Logical instructions will usually reset the flag and arithmetic instructions as well as those that use arithmetic elements (such as compare) will set it or reset it based on the results.

If it’s clear, the bits shifted out were less than half of the LSB, and rounding can be done by truncation. If the carry is set, the bits shifted out were at least half of the LSB. Now, with the sticky bit, we can see if any other bits shifted out during the divide were ones; if so, the sticky bit is set and we can round up. Rounding doesn’t have to be done as described here, but however you do it the sticky bit can make your work easier. Too bad it’s not available on more machines. Branching Your ability to do combined jumps depends on the flags.

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A treatise on differential equations by George Boole


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