System Information
System 1:
OS: Windows 10 32-bit
CPU: Intel Atom Z3740 @1.33GHz
GPU: Intel HD Graphics (Integrated)
RAM: 2.00GB

System 2:
OS: Windows 7 Ultimate 64-bit SP1
CPU: AMD Athlon II X2 270 @2.3GHZ
GPU: ATI Radeon 7000 Graphics (Integrated)
RAM: 8.00GB
(Note: both systems are using a 32-bit build of Blender)

Drivers on both systems are up-to-date.

Blender Version
Broken: 2.79 5bd8ac9 32-bit build (the release version available on the blender.org website)

Short description of error
Blender crashes to desktop mid-render when attempting to perform a denoising operation. The console spits out "Error: EXCEPTION_ACCESS_VIOLATION", implying a problem with memory usage. Memory usage was roughly ~120.00M according to the info bar at the time of the crash. Task Manager reports that Blender was using ~250MB of RAM at the time of the crash, available RAM was ~500MB with plenty of virtual memory to spare.

If it is a memory problem how much memory should the denoising feature really be using?

This crash happens even on simple scenes such as the default startup scene, with render resolutions set to something really low (like 320x240 pixels) and using the smallest tile size possible (8x8), and when using only one thread. The render will complete normally with denosing disabled.

On System 2 the render completes normally with denoising. System 2's Task manager reported Blender was using ~250MB during the render.

Exact steps for others to reproduce the error
Render a scene via Cycles with denoising enabled.