A schedulable memory scrubbing circuit and/or a known-state memory test circuit (collectively, background memory test apparatus (“BGMTA”)) are located on-chip with an integrated computing system. The BGMTA operates in parallel with a system CPU but shares a system bus with the CPU. The BGMTA sequentially reads one word at a time from a block of memory to be tested during system bus idle cycles. The schedulable memory scrubbing circuit embodiment tests on-chip parity/ECC memory arrays using memory controller-implemented parity or ECC error detection to trigger error handling interrupts. The known-state memory test circuit embodiment performs CRC calculations on known-state memory arrays as each data word is read sequentially. A final resulting CRC calculation value is compared to a known CRC value for the block, sometimes referred to as a “golden CRC.” If the two CRC values differ, a CRC error interrupt is triggered for servicing by the CPU.