The program is shown on the simulator below:

We are given the program instructions and the PC at time 0. We use this information to make claims about the program's state at time 1. For example:

• Since the PC is 0 at time 0 and instruction #0 is an ADDI instruction, at time 1, PC is 1.
• Since the PC is 0 at time 0 and instruction #0 is addi dst=3 src=0 imm=3, at time 1, memory cell #3 becomes 3.

Then we use the claims about time 1 to prove claims about time 2, and so on. Eventually, at time 14, we prove that memory cell #5 stores 21 and the program terminates.

Quiz (1 point)

• if the following are true:

  • instruction #0 is addi dst=3 src=0 imm=3
  • the PC at time 0 = 0

  then value of cell 3 at time 1 = 3

• if the following are true:

  • instruction #0 is addi dst=3 src=0 imm=3
  • the PC at time 0 = 0

  then the PC at time 1 = 1

• if the following are true:

  • instruction #1 is addi dst=4 src=0 imm=0
  • the PC at time 1 = 1

  then value of cell 4 at time 2 = 0

• if the following are true:

  • instruction #1 is addi dst=4 src=0 imm=0
  • the PC at time 1 = 1

  then the PC at time 2 = 2

• if the following are true:

  • instruction #1 is addi dst=4 src=0 imm=0
  • the PC at time 1 = 1
  • value of cell 3 at time 1 = 3

  then value of cell 3 at time 2 = 3

• if the following are true:

  • instruction #2 is addi dst=5 src=0 imm=0
  • the PC at time 2 = 2

  then value of cell 5 at time 3 = 0

• if the following are true:

  • instruction #2 is addi dst=5 src=0 imm=0
  • the PC at time 2 = 2

  then the PC at time 3 = 3

• if the following are true:

  • instruction #2 is addi dst=5 src=0 imm=0
  • the PC at time 2 = 2
  • value of cell 3 at time 2 = 3

  then value of cell 3 at time 3 = 3

• if the following are true:

  • instruction #2 is addi dst=5 src=0 imm=0
  • the PC at time 2 = 2
  • value of cell 4 at time 2 = 0

  then value of cell 4 at time 3 = 0

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 3 = 3
  • value of cell 5 at time 3 = 0

  then value of cell 5 at time 4 = 7

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 3 = 3

  then the PC at time 4 = 4

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 3 = 3
  • value of cell 3 at time 3 = 3

  then value of cell 3 at time 4 = 3

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 3 = 3
  • value of cell 4 at time 3 = 0

  then value of cell 4 at time 4 = 0

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 4 = 4
  • value of cell 4 at time 4 = 0

  then value of cell 4 at time 5 = 1

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 4 = 4

  then the PC at time 5 = 5

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 4 = 4
  • value of cell 3 at time 4 = 3

  then value of cell 3 at time 5 = 3

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 4 = 4
  • value of cell 5 at time 4 = 7

  then value of cell 5 at time 5 = 7

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 5 = 5
  • value of cell 3 at time 5 = 3
  • value of cell 4 at time 5 = 1

  then the PC at time 6 = 6

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 5 = 5
  • value of cell 3 at time 5 = 3

  then value of cell 3 at time 6 = 3

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 5 = 5
  • value of cell 4 at time 5 = 1

  then value of cell 4 at time 6 = 1

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 5 = 5
  • value of cell 5 at time 5 = 7

  then value of cell 5 at time 6 = 7

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 6 = 6

  then the PC at time 7 = 3

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 6 = 6
  • value of cell 3 at time 6 = 3

  then value of cell 3 at time 7 = 3

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 6 = 6
  • value of cell 4 at time 6 = 1

  then value of cell 4 at time 7 = 1

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 6 = 6
  • value of cell 5 at time 6 = 7

  then value of cell 5 at time 7 = 7

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 7 = 3
  • value of cell 5 at time 7 = 7

  then value of cell 5 at time 8 = 14

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 7 = 3

  then the PC at time 8 = 4

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 7 = 3
  • value of cell 3 at time 7 = 3

  then value of cell 3 at time 8 = 3

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 7 = 3
  • value of cell 4 at time 7 = 1

  then value of cell 4 at time 8 = 1

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 8 = 4
  • value of cell 4 at time 8 = 1

  then value of cell 4 at time 9 = 2

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 8 = 4

  then the PC at time 9 = 5

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 8 = 4
  • value of cell 3 at time 8 = 3

  then value of cell 3 at time 9 = 3

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 8 = 4
  • value of cell 5 at time 8 = 14

  then value of cell 5 at time 9 = 14

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 9 = 5
  • value of cell 3 at time 9 = 3
  • value of cell 4 at time 9 = 2

  then the PC at time 10 = 6

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 9 = 5
  • value of cell 3 at time 9 = 3

  then value of cell 3 at time 10 = 3

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 9 = 5
  • value of cell 4 at time 9 = 2

  then value of cell 4 at time 10 = 2

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 9 = 5
  • value of cell 5 at time 9 = 14

  then value of cell 5 at time 10 = 14

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 10 = 6

  then the PC at time 11 = 3

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 10 = 6
  • value of cell 3 at time 10 = 3

  then value of cell 3 at time 11 = 3

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 10 = 6
  • value of cell 4 at time 10 = 2

  then value of cell 4 at time 11 = 2

• if the following are true:

  • instruction #6 is jump imm=3
  • the PC at time 10 = 6
  • value of cell 5 at time 10 = 14

  then value of cell 5 at time 11 = 14

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 11 = 3
  • value of cell 5 at time 11 = 14

  then value of cell 5 at time 12 = 21

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 11 = 3

  then the PC at time 12 = 4

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 11 = 3
  • value of cell 3 at time 11 = 3

  then value of cell 3 at time 12 = 3

• if the following are true:

  • instruction #3 is addi dst=5 src=5 imm=7
  • the PC at time 11 = 3
  • value of cell 4 at time 11 = 2

  then value of cell 4 at time 12 = 2

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 12 = 4
  • value of cell 4 at time 12 = 2

  then value of cell 4 at time 13 = 3

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 12 = 4

  then the PC at time 13 = 5

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 12 = 4
  • value of cell 3 at time 12 = 3

  then value of cell 3 at time 13 = 3

• if the following are true:

  • instruction #4 is addi dst=4 src=4 imm=1
  • the PC at time 12 = 4
  • value of cell 5 at time 12 = 21

  then value of cell 5 at time 13 = 21

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 13 = 5
  • value of cell 3 at time 13 = 3
  • value of cell 4 at time 13 = 3

  then the PC at time 14 = 7

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 13 = 5
  • value of cell 3 at time 13 = 3

  then value of cell 3 at time 14 = 3

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 13 = 5
  • value of cell 4 at time 13 = 3

  then value of cell 4 at time 14 = 3

• if the following are true:

  • instruction #5 is beq left=3 right=4 imm=1
  • the PC at time 13 = 5
  • value of cell 5 at time 13 = 21

  then value of cell 5 at time 14 = 21

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.