Logic circuit to handle incrementing by 1
If you're talking about discrete logic, like 7400 series logic, then the chip you're looking for is called a counter. Two 74191 (4-bit up/down synchronous counter) chips cascaded will give you what you want, and there are other chips that do a similar function. 

If you want the most compact way to add '1', then you could use half-adders for each bit instead of full adders. Not too sure about subtraction though.