Because apparently no-one seems to know how to use a block explorer...
Anyway, the good news is that if you indeed sent to this address:
1ADdBfwkJRse2BibjgUAmuchBU6tr3HsP, then your ~3.428 BTC are still there. The only transaction recorded is for the 3rd August 2016 which lines up with your assertion that you:
transferred my holdings of bitcoin from my coinbase account to my electrum wallet back in august
Now, if your Electrum wallet is not showing the balance there are a couple of reasons why... First, the Electrum wallet has not synced.
Is the network indicator in the bottom right corner a "Green Light"?
If it isn't, then there is a chance you're not connected to any Electrum servers (Red Light) or it is busy syncing (the blue recycling symbol)... In any case, click it and you should get a "Network" window pop up... at the top, you can see what the current block height it is at:
If this number isn't 423467 or higher, then your copy of Electrum won't see the transaction (as that is the block that this transaction was included in).
You can also go into the console and type:
and press Enter.
If you don't get "true", then that might explain why it isn't showing.
If all that checks out, then maybe that address isn't part of this particular Electrum wallet... you can go into the console and type:
ismine("1ADdBfwkJRse2BibjgUAmuchBU6tr3HsP")
and press Enter...
if you get "true", then the address is definitely in your wallet... if you get "false"... then this wallet doesn't contain that address and that is why you can't see it. If the wallet doesn't contain that address, then perhaps you created a new wallet between August and now? You'd need to restore your old wallet using the appropriate seed to see the address and balance.
If your wallet contains the address and the network is up to date... then something REALLY strange is going on... Possibly that address was beyond the gap limit for this particular install of Electrum? So when you loaded it up, it only scanned the first 50 addresses and that address was #51 or later?