Proof: JUMP Instruction Example

Let's prove the following theorem:

if the following are true:
  • instruction #0 is jump imm=2
  • the PC at time 0 = 0

then the PC at time 1 = 2

In this example, a JUMP instruction sets the PC to 2, causing the computer to skip instruction #1.

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Proof:

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Given
1 instruction #0 is jump imm=2
2 the PC at time 0 = 0
Proof Table
# Claim Reason
1 the PC at time (0 + 1) = 2 if instruction #0 is jump imm=2 and the PC at time 0 = 0, then the PC at time (0 + 1) = 2
2 0 + 1 = 1 0 + 1 = 1
3 the PC at time (0 + 1) = the PC at time 1 if 0 + 1 = 1, then the PC at time (0 + 1) = the PC at time 1
4 the PC at time 1 = 2 if the PC at time (0 + 1) = the PC at time 1 and the PC at time (0 + 1) = 2, then the PC at time 1 = 2

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