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1).

(a) Given a tiny computer that has a word size of 8 bits, what are the smallest negative numbers and the largest positive numbers that this computer can represent in each of the following representations?  (2+2+2+2=8 marks)
I. One's complement
II. Two's complement
III. Signed magnitude
IV. Unsigned magnitude

(b) Convert the followings:  (7 marks)
I. 0x5AB into Octal 
II. 101101.1012 into Decimal 
III. 12348 into Binary 
IV. 679810 into Base 5 number 
V. 976.6310 into Binary 
VI. 1001001011 into Hexadecimal
VII. 10011110 (8-bit 2’s complement representation) to Decimal

2).

(a) Using basic Boolean algebra identities for Boolean variables X and Y, prove that X’(X+Y)+(XX+Y)(Y’+X)=Y+X. Please show all steps and mention the identities used. (6 marks)

(b) A subject has 4 assessments, such as Assignment, Blog, Discussion Forum and Quiz. In order to pass in the subject, a student must get as below:

  • Assignment component must pass (50 or above)
    • Any 2 more assessments must pass
    • Fail otherwise

Construct a truth table and find the minimized Boolean function. Draw a circuit diagram for the Boolean function

Representation of data in One's complement, Two's complement, Signed magnitude and Unsigned magnitude

1).

a.

  1. One’s complement

-(2N-1-1) to 2N-1-1 : therefore when n=8 we get : -27-1 to 27 - => -127 to 127

  1. Two’ complement

        -2N-1 to 2N-1-1 : therefore when n=8 we get : -27 to 27-1 => -128 to 127

  1. Signed magnitude

        -(2N-1-1) to 2N-1-1 : therefore when n=8 we get : -27-1 to 27-1 => -127 to 127

  1. Unsigned magnitude

        0 to 2N-1 : 0 to 255 (David & John, 2012)

                                                           

                                                                   

                                                                      

V. For 976

           Decimal

              /2

            Remainder

              976

                488  

                   0

              488

                244

                   0

              244

                122

                   0

              122

                61

                   0

              61

                30

                   1

              30

                15

                   0

              15

                7

                   1

              7

                3

                   1

              3

                1

                   1

              1

                0

                   1

Produces -> 1111010000

For fraction part .6310

            Decimal

                /2

            Remainder

               6310

                  3155

                    0

               3155

                  1577

                    1

               1577

                  788

                    1

               788

                  394

                    0

               394

                  197

                    0

               197

                  98

                    1

               98

                  49

                    0

               49

                  24

                    1

               24

                  12

                    0

               12

                   6

                    0

               6

                   3

                    0

               3

                   1

                    1

               1

                   0

                    1

Produces -> .1100010100110

Conversion is : 111010000.1100010100110 (David & Sarah, 2013)

VI.

(10)(0100)(1011)

10  =>   0010   =>  2

              0100   =>  4

1011   => 11  => B

Conversion is 24B (William, Computer Organization and Architecture, 2015)

VII.

10011110 – 1 = 10011101

10011101 is flipped to 01100010

01100010(2) 

(027 + 1×26 + 1×25 + 0×24 + 0×23 + 0×22 + 1×21 + 0×20)

= (64 + 32 + 2)

= 9810

100111102 => -9810 (Linda & Julia, 2014)

(2).

                                                          

                                                                 

                                (CTI, Computer Organization and Architecture, Designing for Performance: Computer science, Computers, 2016)

b)

Assignment = A Blog = B Discussion Forum = C Quiz = D (William, 2013)

A                    B                    C                        D

           Y

0                     0                    0                        0

           0

0                     0                    0                        1

           0

0                     0                    1                        0  

           0

0                     0                    1                        1

           0

0                     1                    0                        0

           0

0                     1                    0                        1

           0

0                     1                    1                        0

           0

0                     1                    1                        1

           0

1                     0                    0                        0

           0

1                     0                    0                        1

           0

1                     0                    1                        0

           0

1                     0                    1                        1

           1

1                     1                    0                        0

           0

1                     1                    0                        1

           1

1                     1                    1                        0

           1

1                     1                    1                        1

           1

                                                                  

Computer Architecture refers to those attributes of a system that have a direct impact on the logical execution of a program. Examples: o the instruction set o the number of bits used to represent various data types o I/O mechanisms o memory addressing techniques ? Computer Organization refers to the operational units and their interconnections that realize the architectural specifications. Examples are things that are transparent to the programmer: o control signals o interfaces between computer and peripherals o the memory technology being used ? So, for example, the fact that a multiply instruction is available is a computer architecture issue. How that multiply is implemented is a computer organization issue. • Architecture is those attributes visible to the programmer o Instruction set, number of bits used for data representation, I/O mechanisms, addressing techniques. o e.g. Is there a multiply instruction? • Organization is how features are implemented o Control signals, interfaces, memory technology. o e.g. Is there a hardware multiply unit or is it done by repeated addition? • All Intel x86 family share the same basic architecture • The IBM System/370 family share the same basic architecture • This gives code compatibility o At least backwards • Organization differs between different versions

References:

CTI, R. (2016). Computer Organization and Architecture, Designing for Performance: Computer science, Computers. Adelaide: Cram101.

CTI, R. (206). The Essentials Of Computer Organization And Architecture: Computer science, Computers. Bunbury: Cram101.

David, A., & John, L. (2012). Computer Organization and Design: The Hardware/software Interface. Wollongong: Elsevier.

David, M., & Sarah, L. (2013). Digital Design and Computer Architecture. Sydney: Elsevier.

GHOSH. (2011). COMP ORG & ARCHITECTURE - WBUT JUNE 2011. Perth: Tata McGraw-Hill Education.

Linda, N., & Julia, L. (2014). The Essentials of Computer Organization and Architecture. Adelaide: Jones & Bartlett Publishers.

William, S. (2013). Computer Organization and Architecture: Designing for Performance. Bundaberg: Pearson.

William, S. (2015). Computer Organization and Architecture. Melbourne: Pearson Education.

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