Beechcraft Premier 1 pilot reported a loss of both ADCs during descent in IFR conditions. The pilot hand flew the approach using standby instruments and landed.

Narrative

Flight from ZZZ1 to ZZZ under IFR flight plan at XAPM central time. Seven soul onboard the plane 1 single pilot Type rated and another pilot type rated observed in the copilot side. We flew at top Altitude FL410; spoke with Center and got the instruction to fly direct to ZZZ2 on the ZZZZ arrival and decent from FL410 TO FL350. ATC ask me what is my Mach speed; I saw 0.73 when I am on tracking. I looked to the copilot PFD and so 0.76 after I notice that my speed indicator on the left pilot side keep decreasing all the way down to stall speed while I am on 90%N1 and descending. Light of IAS on left PFD came also on so I switch to ADC number 2 that looked stable at that time. I run the checklist did as what in it; to switch between the ADC normal to one of the other so I switch to ADC 2.ATC told me to decent to FL240 or FL230. At FL340 I remember I trend on the wing anti ice and engine anti ice because of IMC. After few minutes I lost speed at ADC 2 and the autopilot came off so I hand fly the plane. I [advised] ATC and ask from him if he can give me vectors to an airport with long runway and VFR conditions because I knew all the areas around is IMC and icing condition. I asked ATC to see what he saw as my altitude and he told me to reset my transponder because he do not have indication of my altitude. I reset the transponder and still he did not worked. I flew by the backup ASI and altitude indicator. AHRS worked fine; did not had problem with him. ATC cleared me at first to ZZZ3 and then told me ZZZ4 as better ceiling condition so we diverted to ZZZ4. Around 6000 ft. ADC 2 came alive. ATC told me that he have my altitude on the mode C transponder. ADC 1 still did not worked. I got vectors to Runway XXR from ATC; I loaded the ILS XXR on the FMS. Around 2900 ft. we was outside IMC and saw the runway. We landed VFR at ZZZ4. No one was injured and the aircraft did not damage.