One of the problems found in the design of the electronics for astronomical instruments is the difficulty to find precise digitizers (16 bits) at high speed. In fact, most of the chips which claim to have 16-bit actually have a lower ENOB (Effective Number Of Bits), normally around 14, when considering their noise effects. In this paper, a technique based in auto-adjustable gain amplifiers is proposed as a way to relax the A/D requirements for astronomical CCDs and infrared detectors. The amplifiers will automatically toggle between 2 different gains depending on the pixel value. The technique is based on the fact that, due to the shot (photon) noise of the detectors, the maximum signal to noise ratio achievable in most of these devices is relatively low, allowing the use of A/D converters with an ENOB of only 14 (or even 12) bits when combined with auto-adjustable gain amplifiers. It will be shown that the lower resolution of the A/D converters will not affect the accuracy of the science data, even when many images are averaged out to compensate the effects of the shot noise. Furthermore, given that many real A/D converters do not reach an ENOB of 16, for low level signals the accuracy can be even slightly improved with the technique described in this paper. On the other hand, this relaxing of the A/D requirements can allow the use of off-the-shelf boards for the acquisition systems.