I thought to myself why they didn't want it? Perhaps they were given a DAB clock radio as a gift so they no longer needed it. This clock only used FM radio, the sound in FM radio is transmitted directly into the radio wave so when the signal is absorbed by the antenna, it can be passed across a transistor, the current released by the transistor would be greater than the energy from radio pulse, the electrical output would then pass a copy of the signal to another transistor and be amplified a second time, then a third time. Eventually an analogue signal strong enough for a speaker would be generated. I think that is why they're called transistor radios. DAB is different, the whole signal shuts off completely and then back on again and the delay is timed by a micro chip and represents a data character. The data characters describes how to assemble the sound wave mathematically. The whole signal turning off and on in pulses encodes data, a bit like morse code. A micro processor can extract the data, even if most of the signal is damaged because it isn't using the wave itself for data. You need a micro chip that can understand the signal and data commands to get the sound but the sound in DAB is always in a good condition and they can use more radio bands that are useless for FM signals so you get a lot of stations. DAB radios are more like computers, transistor radios don't need micro processors. They're much more simple, just a simple circuit.
When I looked at my Radio Alarm clock, I saw a beauty in it that most people don't see, a delicate balance between cost and functionality that was established when it was made all those years ago. It had a digital display and memory banks for radio stations so it was using a relatively simple micro chip but it was a simple one that could be made very quickly without too much cost. It had a dial on it to set whether the alarm is the radio or a buzzer or both or none. The fragment digital LCD screen is backlit with orange LEDs so you can see the time, even in the dark. The Radio Alarm and buzzer alarm could be different times, so the radio could turn on, then 15 minutes later the buzzer alarm if you wanted. I could be woken up to BBC radio 4 playing the news and if I'm in a deep sleep, the second alarm would be a buzzer that I set to go off 15 or 20 minutes later. There is also a button on the clock to play the radio on tap. There is a slight curve on every surface of the clock radio and it looks very beautiful to me.
Always go to a charity shop because you may find something you need or like and you're supporting a charity.