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Nvidia Optimus and AMD Hybrid Graphics are examples of this sort of system of switchable graphics. 2021, an increasing number of models use memory soldered to the motherboard. Before 2000, most laptops used proprietary memory modules if their memory was upgradable. In the early 2010s, high end laptops such as the 2011 Samsung 700G7A have passed the 10 GB RAM barrier, featuring 16 GB of RAM. When upgradeable, memory slots are sometimes accessible from the bottom of the laptop for ease of upgrading; in other cases, accessing them requires significant disassembly. Most laptops have two memory slots, although some will have only one, either for cost savings or because some amount of memory is soldered. Some high-end models have four slots; these are usually mobile engineering workstations, although a few high-end models intended for gaming do as well. As of 2021, 8 GB RAM is most common, with lower-end models occasionally having 4GB. Higher-end laptops may come with 16 GB of RAM or more.
An increasing number come with a basic 4GB, though, especially in the $200-plus range. Up at $400 and above, 8GB is common, and some units even manage to include 12GB in under-$700 configurations. Storage is an area you may have to set some firm expectations around, as capacities are seldom very high; these types of desktops are not meant to store huge amounts of files locally. In the cheapest, smallest desktops, you'll get as little as 32GB or 64GB of what's called eMMC flash storage, similar to what's offered in most Chromebooks. MMC; SSDs will feel snappier. Some of the full-size towers on our list include 256GB or even 512GB SSDs, at which point you're hardly compromising any more. We strongly favor SSDs over hard drives, even in this price range. Look for higher-capacity storage if you're a serial downloader, but as evidenced by Chromebooks, internet-connected devices can get away with a lot less local storage thanks to the cloud. Flash storage and SSD will be norm in the really small budget desktops, as these models are too tight inside for conventional 3.5-inch (desktop-size) hard drives, but some can take 2.5-inch (laptop-size) drive upgrades.
Abstraction is defined to a concrete (more precise) model of execution. Abstraction may be exact or faithful with respect to a property if one can answer a question about the property equally well on the concrete or abstract model. ×, is worth modulo n, then one needs only perform all operations modulo n (a familiar form of this abstraction is casting out nines). Abstractions, however, though not necessarily exact, should be sound. That is, it should be possible to get sound answers from them-even though the abstraction may simply yield a result of undecidability. For instance, students in a class may be abstracted by their minimal and maximal ages; if one asks whether a certain person belongs to that class, one may simply compare that person's age with the minimal and maximal ages; if his age lies outside the range, one may safely answer that the person does not belong to the class; if it does not, one may only answer "I don't know".
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