Turing Exercise

Class Exercise: Understanding Pseudocode and the Turing Machine

The Diffusion algorithm

• Inputs:
  • Two end temperatures (TL and TR)
  • A list of 5 starting temperatures.

• Outputs:
  • A list of 5 steady-state temperatures and the heat current.

• Pseudocode:

1. Compute QLA = (TL – TA)/2
2. Compute QAB = (TA – TB)/2
3. Compute QBC = (TB – TC)/2
4. Compute QCD = (TC – TD)/2
5. Compute QDE = (TD – TE)/2
6. Compute QER = (TE – TR)/2
7. Set TA = TA + QLA - QAB
8. Set TB = TB + QAB - QBC
9. Set TC = TC + QBC - QCD
10. Set TD = TD + QCD - QDE
11. Set TE= TE + QDE - QER
12. If there were changes, go to step 1

Task: Choose 1 person as the CPU, and 11 others as memory locations (5 temperatures in the first row and 6 Q values in the back row). The CPU runs through the algorithm one step at a time and issues instructions to the memory locations (who hopefully remember their numbers).

Assume the starting conditions are:

TL=500	TA=100	TB = 200	TC=300	TD=400	TE=500	TR=100
QLA	QAB	QBC	QCD	QDE	QER (undefined values at start)

Notes

Our class was able to achieve all 12 steps in about 5 minutes, giving us a processor speed of 0.04 operations per second (compare to giga-flops…).