Cessna 310 pilot reported a ground conflict after failing to give way to a taxiing King Air aircraft as instructed by Tower. Reporter stopped just in time to avoid a possible collision.

Narrative

I flew a visual approach into ZZZ runway XX and landed normally. The tower told me to turn off the runway at taxiway 1 and take taxiway 2. I was told to give way to the King Air taxiing out from the ramp. As I was moving southwest on taxiway 1; I was looking toward the ramp from my 12 o'clock to my 2 o'clock to find the King Air.I was nearly at the end of taxiway 1 at taxiway 2. Much to my shock I spotted the King Air in my peripheral vision at my 9 o'clock taxiing northwest on taxiway 2! I stomped on the brakes to the max to stop just as the King Air taxied from my left to my right.Thank the Lord I stopped just in time! I thought I was going to have a heart attack. The tower and the King Air were doing everything right. I should have been scanning from 9 o'clock to 3 o'clock as I was taxiing; and not focusing just on the ramp. I apologized to the tower for screwing up so bad.I made a huge mistake by just looking at the ramp area instead of keeping my eyes high; wide; and glancing everywhere as I taxied. I feel terrible for how bad I did--there could have been an awful crash and I would have caused it.