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Radar isn't a very old technology. Developed during WW2, it is 70 years old. Early radar was just to detect objects in the air. This was done by transmitting a powerful signal and waiting for the reflection from the flying object. The time between transmission and reception was twice the distance of the object. The position of the antenna provided the angular position. Something we still display even on modern systems. Such traditional systems are called primary radar.
However, due to geometry the altitude resolution on primary radar was not provided (or very inaccurate in systems with several beams). Also, if two aircraft were flying nearby, there was no identification provided for those bright spots on the screen. Due this demand a system was introduced permitting the aircraft to modify the received pulse: Using 12 bits, it returns either altitude or the squawk identification. The radar station has two request patterns which it transmits towards the aircraft, and the aircraft responds with either a Mode-A pattern for squawk or a Mode-C pattern for altitude. The pattern itself does not contain any information about its kind, so only the one who has requested that info will know how to post process. As a passive receiver such as we are, it is that we only hear a number between zero and 4095, but we don't know the question.
With growing air traffic, air traffic controllers required more information about the aircraft. Also, they wanted to get control over the transmissions in a crowded airspace. This is when Mode-S became introduced. Not at least the "S" stands for "Selective". Mode-S transmissions contains some more information like higher resolution altitude, aircraft capabilities and identification. As a passive listener we now got the capability to distinguish between several formats and collect information about each single aircraft.
Last, one special frame format within the Mode-S protocol, so called DF-17, became introduced to indicate the position of the aircraft and some more information. In fact ADS-B is only one message within Mode-S. It requires 2 DF-17 frames to calculate the position unambiguous, the so called even and odd formats.
Our Radarcape and the Mode-S Beast can receive Mode-AC messages and output them on the binary ports. But these messsages do not have position information within. They cannot be used for localisation within the processing capabilities of a Radarcape.
Also Mode-S does not contain location information, but as they have enougth information to distinguish among each other and combining data of at least 3 Radarcape with a precision time stamp and a process called Multilateration (MLAT) we are able to estimate the position of the aircraft from Mode-S transmissions.
Finally, using ADS-B transmissions, the aircraft directly tells us where it believes to be or where it wants us to think it currenly is.