Proof: JAL Instruction Example
Let's prove the following theorem:
if the following are true:
- instruction #5 is a JAL instruction with jump to: 1
- the PC at time 2 = 5
then the PC at time 3 = 1
In this example, a JAL instruction causes the computer to jump to instruction #1.
Instructions
Memory Cells |
---|
Program Counter | Time |
---|---|
0 | 0 |
LW Computer Simulator
Proof:
Given
1 | instruction #5 is a JAL instruction with jump to: 1 |
---|---|
2 | the PC at time 2 = 5 |
# | Claim | Reason |
---|---|---|
1 | the PC at time (2 + 1) = 1 | if instruction #5 is a JAL instruction with jump to: 1 and the PC at time 2 = 5, then the PC at time (2 + 1) = 1 |
2 | 2 + 1 = 3 | 2 + 1 = 3 |
3 | the PC at time (2 + 1) = the PC at time 3 | if 2 + 1 = 3, then the PC at time (2 + 1) = the PC at time 3 |
4 | the PC at time 3 = 1 | if the PC at time (2 + 1) = the PC at time 3 and the PC at time (2 + 1) = 1, then the PC at time 3 = 1 |
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