ICT114: Analyze and Explain the Various Number Representations of digital Systems : Computer Architecture Homework, SUSS, Singapore

Question 1 

A digital system uses 8-bit for integer representation and 16-bit for floating-point number representation. Analyze and explain the various number representations and answer the following questions.

a. Given A = 5A16 and B = 8D16.

(i). If 8-bit sign-magnitude representation is used to represent integers, what is the range of decimal values it can represent?

(ii). Express the value of A and the value of B in 8-bit binary if sign-magnitude representation is used for integers.

(iii). Show how the digital system computes the logic operation A XOR (A OR B). Express the result in hexadecimal.

b. Given X = 5510 and Y = -6610.

(i). Express the value of X and the value of Y in 8-bit binary if sign-magnitude representation is used for integers.

(ii). Express the value of X and the value of Y in 8-bit binary if 2’s complement signed integer representation is used.

(iii). Find the result of X + Y by performing the computation in 2’s complement arithmetic. Convert the result to decimal and show it is equal to -11.

c.  The hexadecimal number C0FE represents a 16-bit floating-point number. Its representation is given in Figure Q1(c). What is the decimal value? Show your work.

Question 2
Figure Q2 shows the characteristics of a hypothetical machine, relevant portions of memory, processor registers, and some I/O devices. For the instruction format shown in Figure Q2(i), if it is an I/O instruction, bits 4 to 15 identifies a particular I/O device, else a memory address.

(a) How many memory locations can this processor address?

(b) This hypothetical machine is to execute the following program:
1. Load AC from device 9.
2. Add contents of memory location 888.
3. Store AC to memory location 889.

There are three fetches and three execute cycles. The process can be divided into six steps or cycles. For each step or cycle, demonstrate what happens and list the contents of the following registers:

(i) PC at the start of each cycle,
(ii) AC at the end of each cycle and
(iii) IR at the end of each cycle.

Assume the initial values are as given in Figure Q2(v). Summarise your answer using the format given in Table Q2.

Question 3
This question is based on the EASY68K simulated processor. Assume the contents of all data and address registers are equal to zero before the start of the program. All numbers are hexadecimal.

Demonstrate how instructions of the program are executed by using the E114 Processor Instruction Set of the EASY68K simulator.

Figure Q3 shows a program segment based on the course’s simulated processor. The program is to determine the average of a series of integers stored in an array. Assume the average is an integer, ignoring the fractional parts.

Note: Instruction Logical Shift Right (LSR) shifts the contents of register D1 by 3 bits to the RIGHT.

(a) Identify the addressing mode used in each of the following instructions.

(i) MOVE.B #$08, D0

(ii) ADD.B (A0)+, D1

(iii) LSR #$03, D1

(iv) MOVE.B D1, $2050

(b) The program includes a loop. Which register is being used as a loop counter and how many times in total will the set of instructions within the loop be executed?

(c) From which instruction(s) do you deduce the answers for Q3(b)?

(d) The loop picks up successive data items from a block of locations in data memory.  What are the lowest and highest addresses (in Hex) of the locations in this block?

(e) Explain the purpose of the instruction LSR #$03, D1 in relation to the function of the program.

(f) Rewrite the program in Figure Q3 to include a subroutine to add a series of integers. The subroutine should perform the functions of the loop. The subroutine occupies memory space just below the main program. Use SUM as the subroutine address label. Initialize and use test data: 1, 2, 3, … up to the loop counter deduced in

Q3(b). Assume the contents of all data registers are set to zero before the start of the program. (Reminder: All numbers including the test data are in hexadecimal.) Test your program with the course’s simulator. Once it is working correctly, copy and paste the source code of your program to your MS WORD answer document.

(g) Submit a screenshot of the memory contents that include addresses from 1FF0 to 2060 when the program stops. Use the instructions given below to obtain the screenshot. Instructions:

1. To view the memory contents at the simulator screen, click on the View menu and select Memory. Click on the Page down button to the required addresses. Verify that the memory contents are indeed correct.

2. To capture the ‘screenshot’ select the window, press + on your computer keyboard, and then paste it onto your word document.

Question 4

(a) A computer system uses a 20-bit address bus and can address an 8-bit wide memory. The memory of this computer system contains two 32 Kbytes of ROM (ROM1 and ROM2) and two 16 Kbytes of RAM (RAM1 and RAM2). The memories are ordered in an interlaced manner – ROM1, RAM1, ROM2, and RAM2 and form a contiguous block of memory starting at address 0. The rest of the address range after RAM2 is not used.

Draw a memory map for the computer system. Indicate the starting and ending addresses in hexadecimal for each block of memory and any unused space. Show how the memory addresses are obtained.

(b) Explain the TWO (2) approaches to deal with multiple interrupts.

(c) Describe TWO (2) problems faced by a computer system with single-bus architecture.