Homework on Diodes and Adders (solutions)

Feel free to work on the homework in groups. The work you hand in, however, should reflect your understanding of the material and be in your own words.Students who turn in identical (or close to identical) homework assignments will be asked to explain their answers orally to the TA or prof. A student who cannot explain how he or she arrived at a given answer will be charged with academic dishonesty.

You should justify all of your answers for full credit.

Diodes and Transistors

A schematic diagram of a p-n junction is shown below. The connection to the p side is at point A, and the connection to the n side is at point B.

1.	In which side (p- or n- ) of the depletion layer of the junction will electrons have a higher energy (and thus a lower electric potential)? Explain why this is so and draw a picture showing the appropriate energy levels and the direction of the electric field at a p-n junction. In the depletion layer, the electrons on the p-side will have a higher energy. There are no free electrons (or holes) in the depletion layer - all of the electrons are in the valence band - and the valence band of the p-side is a higher energy state than the n-side because the p-side is negatively charged. (Each conduction electron that leaves the n-side fills a hole on the p-side, thereby increases the energy of the p-side and decreasing that of the n-side. )
2.	To which point (A or B) should you connect the positive terminal of a battery and to which should you connect the negative terminal if current is to flow through the device? Point A. The positive terminal should be connected to the p-side, lowering the energy of that side enough that free electrons from the n-side can make it across.
3.	Explain why current will not flow if the terminals are connected in the opposite way. If you instead raise the energy of the p-side (by connecting the negative terminal to it), the free electrons from the n-side will not be able to cross, and there are no free electrons on the p-side.
4.	You received a handout about how computers perform math, and Turton also discusses calculations in Chapter 4. How many transistors are used in a half-adder (which adds two bits)? How many are used in a full-adder (which adds three bits)? Justify your answer. A half-adder needs an AND gate (3 transistors) and an XOR gate (8 transistors), for a total of 11 transistors. A full-adder needs two half-adders plus an additional OR gate (4 transistors), for a total of 26 transistors.
5.	Use your answer to the previous question to calculate how many transistors are needed to add two 8-bit numbers. The largest 8-digit decimal number is 99,999,999. This number is smaller than 2²⁷ so it can be expressed as a sum of 2²⁶ and smaller powers. This then means 27 binary digits are required (including a digit for 2⁰). Adding 27 bits uses 1 half-adder and 26 full-adders, for a total of 11 + 26 x 7 = 193 transistors.