Question

Elements of Computer Organization

In the following exercise you will practice working with binary numbers and creating digital circuits. The answer should be submitted electronically, you have the choices how to produce the answers: draw by hand and take photo/scan the drawing, then insert the image into a Word file, and save that file as a .pdf - but the most preferable way would be for you to design your circuit using software. You can use either LogiSim (Links to an external site.) or logic.ly (Links to an external site.)to generate your circuits which you may export as a .png or take a screenshot of respectively.

Hexadecimal (4 pts)

Hexadecimal numbers are numbers in base 16. They use the following sixteen digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. They are widely used in computing, for example, to represent colors or network addresses of computers.

1. Convert A2F13₁₆ to decimal. Show your work.
2. Convert 4567₁₀ into hexadecimal. Show your work.
3. Convert 0001010110001100₂ to hexadecimal. Explain how can you use the fact that 16 = 2⁴?
4. If you convert a 64-bit binary number into hexadecimal, how many hexadecimal digits does it have? Explain.

Circuit Design (8 pts)

In this exercise you will design part of a circuit for adding three bits x, y and cin, resulting in two outputs coutand s that represent the addition x+y+cin. This is the same as the full adder that we covered in class. In class, we designed the half-adder and built an incrementer from it. In this lab, you will build a full-adder.

You can break this into two parts. First, design a circuit for computing s, the odd parity function corresponding to the sum bit. You can design your own truth table for s or find it in ZyBooks. Then you should write a corresponding minterm expansion logical formula, and then draw the corresponding circuit.

Next, design a circuit for computing cout, the carry bit. Once again, you can design your own truth table or use the one in ZyBooks. Then, write a corresponding minterm expansion logical formula, and draw the corresponding circuit.

If you simplify your boolean expression, show your work!

Answer 1

As there are multiple questions, answering first 4. For others, please create seperate question

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