TAOCP 1.3.1 Exercise 4
The sign in the address field is part of the instruction encoding and is not constrained by the requirement on memory references.
Section 1.3.1: Description of MIX
Exercise 4. [00] The last example in (5) is LDA -2000,4. How can this be legitimate, in view of the fact that memory addresses should not be negative?
Verified: yes
Solve time: 51s
The sign in the address field is part of the instruction encoding and is not constrained by the requirement on memory references. The instruction format allows the address to be a signed quantity $\pm AA$, so $-2000$ is a legitimate value stored in the instruction word.
The restriction $0 \le M \le 3999$ applies to the effective address used for accessing memory, not to the raw address field before indexing. In the example LDA -2000,4, the index register $rI_4$ supplies a correction so that the computed effective address $M = -2000 + rI_4$ lies in the admissible range of memory locations. This makes the instruction well-formed even though the encoded address field is negative. ∎