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Let's start by looking at the heart of the system — the processor. In this case, the processor is not going to be just the CPU, but also features a built in GPU. This makes the build both cheaper and easier.
For this build, I've chosen AMD's A4-5300 Trinity APU. This is a 3.4GHz — 3.6GHz when in Turbo mode — dual-core part, which also comes equipped with a DirectX 11-enabled Radeon HD 7480D.