Essay: Computer Organization And Architecture: Representation And Boolean Algebra.

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

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

2. Two’ complement

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

3. Signed magnitude

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

4. Unsigned magnitude

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

V. For 976

Produces -> 1111010000

For fraction part .6310

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)

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.