Digital Computer System, Signed Binary Number Representations - Engineering Assignment Help

Assignment Task:

Task:

Question 1
(a) In a digital computer system, signed binary number representations are used to encode negative numbers to its binary form where the negative numbers are expressed as 2’s complement of the corresponding positive number. Table Q1a below shows a set of three signed decimal numbers.

Table Q1a. Set of Signed Numbers
Signed Decimal Number

– 102
+ 35
– 46

Show explicitly how the three signed decimal numbers can be added using 2’s complement approach. Draw ONE (1) conclusion from the answer that you have obtained.

(5 marks)

(b) A combinational logic circuit can generally be referred as a digital logic circuit that combines the function of various basic logic gates such as NOT, AND, OR gates to perform a more complicated logic operation as assigned by its Truth Table. Figure

Q1b shows an example of a combinational logic circuit with three inputs (ABC) and one output (X), and its associated Truth Table.

Truth Table
A B C X
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
Figure Q1b. 3-inputs Combinational Logic Circuit and Truth Table

(i) By selecting another suitable example, describe thoroughly the procedures of converting the logic function assigned in a Truth Table to its most simplified logic circuit form. Support your answer with appropriate illustration for each stated procedure. Note that the example provided must contain FOUR (4) inputs, ONE

(1) output, and the output must show a HIGH signal for any SIX (6) combination of the inputs.

(10 marks)

(ii) Based on your answer in Q1b(i), show explicitly how the logic circuit can be implemented by using only 2-inputs NOR gates. Make sure that the logic circuit is in its simplified form with minimum number of 2-inputs NOR gates. 

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