Following a transient failure of ADC info to both pilot NAV displays the Captain noted a low airspeed indication; which required slats to be extended. Shortly after doing so; the Captain's display returned which showed their actual speed to be well above the maximum slat extend limitation and they received a SLAT OVERSPEED aural warning.

Narrative

While descending through FL300 with autopilot on; the autopilot and autothrottles shut off and both NAV screens went blank. An ADC2 Fail message was displayed on the FMS. I took hand control of the aircraft; continued the descent and requested direct PBG VORTAC because of our RNAV failure. I assigned the pilot not flying troubleshooting duties and instructions to reference the EPC.Approximately 30 seconds later I noted that both ASIs indicated 180 KTS; I immediately commanded 'SLATS EXTEND FLAPS ZERO' to meet configuration requirements for the indicated airspeed. Within about 10 seconds the Captain's ASI returned to normal function and displayed 270 KTS and Mach .68 along with the 'SLAT OVERSPEED' aural warning. Realizing that the initial 180 KTS was false; I commanded 'SLATS RETRACT.' The Captains ASI indicated correctly thereafter; however the First Officer's ASI failed all the way to 0 KIAS and became 'FLAGGED.' The aircraft was hand flown to landing; and a slat inspection was performed prior to re-dispatch.