What does 011111100 refer to in this LC-3 Code?

Question

Okay so I am looking at an example program in LC-3 and one line of code is as follows:

0010 0 10 011111100 ; R2 <- M[x3100]

So I understand that the code is taking the contents at address x3100 and storing them into R2, however I am confused as to how they acquired the offset part of the binary code. When I look up 01111110 in binary, it's 252 with hex number being FC. So how does this relate to the x3100?

Answer 1

The immediate, referred to as the PCOffset9 in some texts, is a pc-relative offset. Thus, the more complete program is probably something like this:

      .ORIG x3000
3000  ...
3001  ...
3002  ...
3003  LD R2, #252
      ...
      ...
3100

      .END

When this instruction executes, the PC holds the value x3003, which is used to fetch the instruction LD R2, #252 from memory. During that instruction's execution, first the PC is used to fetch the instruction, then it is incremented, and next, the "effective address" is computed as ea = PC + PCOffset9 . Here PC is x3004 (was x3003 then +1), and the immediate is xFC, so their sum is x3100. That same offset #252 will refer to a different memory location, if used in another instruction (ie at a location other than x3003). Note that the PCOffset9 is a 9-bit field that is signed: before the above addition to the PC, it is sign extended to 16-bits. Being signed it can reach forwards & backwards, so the range is -256 to +255.