Hardware And Computer Organization

 

Q1. (6 points) A full-adder is a combinational circuit that forms the arithmetic sum of three input bits. It consists of three inputs, x, y, z, and two outputs, C and S. Two of the input, that is, x and y, represent the two significant bits to be added. The third input, z, represents the carry from the previous lower significant position. The output S denotes the sum of two bits and C denotes carry. Answer the following sub-questions.

1) Construct a truth table for the Full-Adder

2) Based on the truth table, construct a K-map for the output S and derive a Boolean equation using K-map. Make the equation as simple as possible.

3) Based on the truth table, construct a K-map for the output C and derive a Boolean equation using K-map. Make the equation as simple as possible.

4) By algebraic manipulation, show that S can be expressed as the exclusive-OR of the three input variables. That is, show that,

S = x XOR y XOR z.

You can prove by deriving from S = x XOR y XOR z to the answer you got in the question 2)

5) By algebraic manipulation, show that C can be expressed as the following term.

C = xy + (x XOR y)z.

You can prove by deriving from C = xy + (x XOR y)z to the answer you got in the question 3)

6) Based on 4) and 5), draw a circuit for the full-adder in Logisim simulator, attach the image file and submit the circuit file!

Q2. (4 points) A sequential circuit has one D flip-flop and one JK flip-flop, two inputs x and y, and one output z. A is the output of D flip-flop, and B is the output of JK-flip-flop; A and B together form the “output state” of the circuit. The flip-flop input equations and the circuit output are as follows. Here DA is the D input of the D-flip flop of A, and JB, KB is the J and K input of the JK-flip flop of B.

DA = ~xy + yB

JB = ~yB + xy

KB = xB + ~yA

z = x+~xy

1) Draw the logic diagram of the circuit and test it with Logisim.

Please attach the circuit image and the generated table!

Please also submit the circuit file!
2) Construct a state diagram of this circuit.

Q3. (10 points) Design a system with the following state changes: This is a sequential circuit with three flip-flops. The state sequence is changed with a clock as in the order of, 111, 010, 100,110, 001, 011, 101, 000, 111 and repeat. Use JK flip-flops.

1) Draw a state diagram.

2) Construct an excitation table .

3) Draw K-maps and derive Boolean equations using K-maps. Make the equations as simple as possible.

4) Draw the system in Logisim simulator, attach the circuit image and submit the circuit file.

5) Test the system and attach the generated table.

Sample Solution

We can reduce, reuse and refuse plastic packaging whilst advocating the development to a circular economy. Say no to plastic bottles, packaging and bags whilst shopping. The environmental advantages to recycling are also obvious as it helps to reduce landfill waste, produces fewer greenhouse gases and recycled products can just as reliable as those made from new materials. (Decker, et al., 2014, pp 46-47)

The Government are starting to make effective changes in relation to plastic use. Scotland are to become the first nation to ban plastic straws after businesses such as Wetherspoons, Wagamamas and McDonalds’s are all trialling the replacement of paper straws. This topic has become a major talking point within the Scottish Government after the introduction in October 2015 to charge 5p for plastic bags. This proposal proved to be a success as the use of plastic bags has reduced by 85%. (Gabbatiss, 2017) Theresea May has also urged a new policy on plastic free aisles in supermarkets which is a goal she aims to achieve within the next twenty-five years. She aims to extend the plastic bag charge to other plastic uses such as takeaway boxes. However, many environmental groups have expressed their views stating that these ambitions need to be promoted by legal legislation. (Walker, 2018) There are many practical steps that the Government are taking to help tackle such a prominent issue and this can also be researched further as new proposals are made.

There is great scope for further exciting research within many areas of this broad topic. This will include specifically how the textile industry can reduce the use of plastic and what alternatives we can create as designers which will support the future to a circular economy. Many more artists and designers are expressing their powerful opinions on the topic; therefore, this area also needs further inquiry. Also, an interest lies in how microplastics are entering our food chains and how this can affect the human body in negative ways. In addition, more research is needed to investigate the link between oil consumption and plastic production. As new laws are introduced by the Government, there is potential for new research as the plastic pollution problem is at the forefront of global issues.

In conclusion, we must focus on human consumption, modern material uses and environmental change to reduce plastic waste in our oceans. The ocean has an influence on each of us in daily life. It provides us with the water we drink, the food we eat and the wildlife we adore. (Decker, et al., 2014, p92) Plastic has many positives and negative uses so we must learn to get the balance of production right. Many companies and brands are setting a positive example for the future and this is led by new government initiatives. We are all aware of the small steps we can take to engage with the challenges of marine pollution. We all assist in the problem therefore everyone can and must help solve it for our future generations. It will never be an easy task but with improved individual actions, industry leadership, design innovation and scientific change it can become a solvable problem. (Decker, et al., 2014, p118)

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