Program counter format LC-2

Question

Not really sure if this is an exact CS question. I'm reading the Patt/Patel Introduction to computing systems Powerpoint presentation and I don't understand about the program counter and instruction register format in LC-2.

On the memory pages section in chapter 5, it writes there: "Direct mode addressing gets page number from PC[15:9] and page offset from IR[8:0]." My question is, I don't understand why the format of PC and IR is in [x:y], can anyone explain it to me? I read on Wikipedia and it says that it should be base + offset, but why does the base and offset both have 2 separate values?

Thanks.

Answer 1

The notation is as follows: FROM[left bit : right bit], so in your example PC[15:9] means take bitfield (number) from PC from fifteenth bit to ninth bit, inclusive, so 15 - 9 + 1 = 7 bits.
The same applies for IR[8:0] meaning take bitfield from IR from eight to zeroth bit inclusive.
For example PC[14:14] would be exactly one bit long and in such case by convention one would write PC[14].