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# Thermodynamics of Computer Homework 1 solution

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1
ECSE 310 Thermodynamics of Computer
Homework 1

(Each question has the same weight)
1. Briefly define the following:
a) kWh
b) CO2e
c) GHG
d) Activity factor (for microprocessor)
e) Dynamic switching energy
f) N-type and p-type semiconductor
g) NMOS and PMOS (draw symbols, mark current direction, source, drain)
h) CMOS
i) Local interconnect

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1
ECSE 310 Thermodynamics of Computer
Homework 1

(Each question has the same weight)
1. Briefly define the following:
a) kWh
b) CO2e
c) GHG
d) Activity factor (for microprocessor)
e) Dynamic switching energy
f) N-type and p-type semiconductor
g) NMOS and PMOS (draw symbols, mark current direction, source, drain)
h) CMOS
i) Local interconnect
j) Global interconnect
k) Sheet resistance
a) Describe why capacitor and inductor can give delay.
b) Use a formula to explain why IBM airgap process is better (in terms of switching speed and
switching energy).
c) Why is it more convenient to use sheet resistance to model interconnects?
3. The current leader of the Top500 supercomputer table (https://www.top500.org/lists/2017/11/ ) is
the Sunway TaihuLight (National Supercomputing Center, Wuxi, China), which has a peak performance
of 125*1015 Flop/s (“Flop/s” means floating point operations per second, which characterizes
computing device performance) and a power consumption of 15,000 kW.
a) Calculate the number of computations per kWh
b) Given that an average Canadian home consumes 11,000 kWh per year of electricity, how many
homes could be run on the power consumed by this supercomputer?
4. a) Using the model for interconnect power given in class (in the notes, lecture 2.2: Interconnect
(III)), extend the model to obtain equations for i) interconnect delay and ii) energy for a
buffered line, where we divide the total line length L into N segments.
b) Obtain an expression for the value of N which minimizes the delay
2
c) Plot delay and energy as a function of N for the following parameters: Cin = 0.89 fF, RL = 0.04
Ω/square, CA = 50 aF/µm2
, C0=5 x Cin, Rin = 14 kΩ, V = 1 V, w = 0.1 µm, L = 50 mm and validate the
expression you obtained in (b) above.
5. The Intel 8086 microprocessor was introduced in 1978. It had an initial clock frequency of 5 MHz, and
had 29,000 transistors, made with 3 μm technology operating at 5 V. The die size was 33 mm2
. Assume
a switching energy per transistor of 1 pJ. The design power was 1.9 W.
a) Estimate the capacitance of the transistors from the data above
b) Assuming an activity factor of 0.1. estimate the power dissipation due to transistor switching
c) For the given thermal design power of 1.9 W, what was the power dissipation per unit area?
d) Assume the same technology is now scaled down to 22 nm transistors, but that the die size
remains the same (i.e. the number of transistors per chip is increased commensurately—
although that’s not a real life scenario). Assume the activity factor remains the same. Estimate
the:
• Number of transistors
• Clock frequency
• Switching energy per transistor
• Total power dissipation due to transistor switching
• Voltage
Which of these values have not been achieved in practice? Why?
e) Assuming an operating voltage of 1 V (but keeping number of transistors and clock frequency as
estimated above), estimate the switching energy per transistor and the associated power
dissipation for the chip.