Refer to figures.
An ILS localiser uses two lobes of differently modulated signals, one is modulated at 150 Hz and the other at 90 Hz, the ILS receiver on an aircraft interprets the amount of each signal as an indication of how far the aircraft is from the centre of the localiser, and on which side. This indication is shown directly on the display. The OBS (Omni Bearing Selector) which is used for VOR radial tracking does not have an impact on the displayed ILS readings. Using an omni-bearing indicator (OBI) display will always give a simple, fly left or fly right, localiser display no matter the chosen OBS course.

A Horizontal Situation Indicator (HSI) has a simple Course Deviation Indicator (CDI) in the middle of the slaved gyro compass, which can be turned to face any direction, on the gyro compass, but when receiving ILS signals will only produce exactly the same display as the standard OBI, fly left or fly right. The direction of the CDI does not affect the CDI indications, just how we view them. The CDI in the figures is for illustration purposes only, to show the different instruments, as requested by a student. It is not currently indicating a ILS, but would look exactly the same with the addition of a glide slope.

When using a ILS back-course, the usual signal lobes are reversed, so an OBI display will be absolutely reverse sensing. This is the same for the CDI in the centre of the HSI, reverse sensing indications. However, the CDI in the middle of the HSI can be turned to face the front course of the standard ILS (needle pointing downwards when flying the back-course) which reverses our view of the indications again. This gives correctly sensing localiser indications for the HSI during a back-course approach, only if the CDI is set to the course of the standard inbound ILS.