Single error detection means your computer stores a parity bit with each word. If ANY single bit in the entire word has flipped, that 'single-bit error' can be detected. Checking Hardware works by 'adding up' the number of binary one-bits turned on in a word, and making sure the check bit is set so that, for example, there is always an ODD number of bits in every word. This is Odd Parity. It is helpful, but limited.
Parity can be also be computed on subgroups of bits. Groupings are chosen very methodically. Then, in addition to overall parity telling you some error occurred, you can figure out which bit is in error. Hardware can be called into action to correct the wrong bit and make it right almost instantly.
The number of additional check bits required depends on the width of the data word. For the 64-bit words in your Mac Pro an additional eight bits is enough to store the additional check bits needed, but a lot of support Hardware must be added in the processor to make it work. at this wring, only Intel Xeon processor implement Error Correcting Code (ECC) memory.
As a side effect, you can also now detect -- but NOT correct -- when a double-bit/uncorrectable error occurs. double-bit errors cause your Mac to halt with a kernel panic, machine check, detected by multiple processors. This prevents this memory error from poisoning your data.
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When the hardware detects a single-bit error-correction event, status bits are set that can allow the number and location of those errors to be tabulated.
The Power-On Self Test runs for only a few seconds. If, in those few seconds, ANY error-correction events have occurred in that short time, the module that incurred those events is marked "absent". Its memory will not be used. The system is told the slot is "empty".
The modules marked absent are no longer operating without errors. They are NOT GOOD ENOUGH to be trusted with your precious data. They are BAD.
Most users feel compelled to remove and re-seat such modules. This simply puts off the inevitable -- Those modules need to be removed from your Mac. If you want the same amount of memory you had before, NEW modules must replace the ones found BAD.