This proof shows that when an ADDI instruction is executed, the Program Counter (PC) increments by 1. Specifically, when the PC is 1, it is incremented to 2.

Note that src imm, and dst are left as variables because these values do not affect the PC. In other words, this property is true regardless of the values of src, imm, and dst.

For reference, here is the simulator. We cannot use variable values in the simulator so src, imm, and dst are given numerical values. Initially, the PC is 0, then 1, and finally 2.

Quiz (1 point)

• 1 + 1 = 2

• if the following are true:

  • instruction #x is addi dst=s src=d imm=imm
  • the PC at time t = x

  then the PC at time (t + 1) = x + 1

• if 1 + 1 = 2, then the PC at time (1 + 1) = the PC at time 2

• if the following are true:

  • a = b
  • a = c
  • b = d

  then c = d

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.

Step	Claim	Reason (optional)	Error Message (if any)
1
2
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