Proof: Add Insn 10
Let's prove the following theorem:
if the following are true:
- the PC at time 10 = 4
- instruction #4 is
add dst=3 src1=1 src2=2
then value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10)
Instructions
Memory Cells |
---|
Program Counter | Time |
---|---|
0 | 0 |
LW Computer Simulator
Proof:
Given
1 | the PC at time 10 = 4 |
---|---|
2 | instruction #4 is add dst=3 src1=1 src2=2 |
# | Claim | Reason |
---|---|---|
1 | value of cell 3 at time (10 + 1) = (value of cell 1 at time 10) + (value of cell 2 at time 10) | if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 10 = 4, then value of cell 3 at time (10 + 1) = (value of cell 1 at time 10) + (value of cell 2 at time 10) |
2 | 10 + 1 = 11 | 10 + 1 = 11 |
3 | value of cell 3 at time (10 + 1) = value of cell 3 at time 11 | if 10 + 1 = 11, then value of cell 3 at time (10 + 1) = value of cell 3 at time 11 |
4 | value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10) | if value of cell 3 at time (10 + 1) = value of cell 3 at time 11 and value of cell 3 at time (10 + 1) = (value of cell 1 at time 10) + (value of cell 2 at time 10), then value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10) |
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