Question 1:

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

(a) Given A = 2A₁₆ and B = 6E₁₆.

(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 A0FF represents a 16-bit floating point number. Its representation is given in Figure Q1(c). What is the decimal value? Show your working.

Question 2:

(a) A hypothetical computer system has a 16-bit address bus and can address an 8-bit wide memory. The memory of this computer system contains two 4 Kbytes ROM chips (ROM1 and ROM2) and two 8 Kbytes RAM chips (RAM1 and RAM2). ROM1, ROM2, RAM1 and RAM2 form a contiguous block of memory starting at address 0. R0M1 occupies the lowest address range. The rest of the address range after RAM2 is not used.

(i) Summarise the address space by drawing a memory map of the computer system. Indicate the starting and ending addresses in hexadecimal for each ROM and RAM chips and any unused space. Show how the memory addresses are obtained.

(ii) Compute the total capacity of the RAM chips in bits. Express your answer in power of 2.

(b) Describe the characteristics and operations of a multiplexed bus interconnection in a computer system.

Question 3:

Figure Q3 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 Q3(i), if it is an I/O instruction, bits 4 to15 identifies a particular I/O device, else a memory address.

Program counter (PC) = Address of instruction
Accumulator (AC) = Temporary storage
Instruction register (IR) = Instruction being executed
(iii) Internal CPU registers

0010 = Store AC to memory
0011 = Load AC from I/O
0101 = Add to AC from memory
(iv) Partial list of opcodes

Figure Q3

(v) Contents of memory, registers and I/O devices at start of program

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

(b) This hypothetical machine is to execute the following program:

1. Load AC from device 5.
2. Add contents of memory location 750.
3. Store AC to memory location 751.

There are three fetch 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 Q3(v).

Question 4:

(a) (i) Given X = 5. Express -X in 8-bit 2's complement representation. 

(ii) Explain the steps or procedures taken to obtain the 2's complement representation. 

(b) Figure Q4(b) is a subroutine for the course's simulated processor. Assume all numbers are in hexadecimal.

Figure Q4(b)

Use the T121 Processor Instruction Set of the EASY68K simulator to answer the following questions.

(i) The subroutine 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? 

(ii) From which instruction(s) do you deduce the answers for Question 4(b)(i)? 

(iii) 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? 

(iv) What is the function of the block of instructions that make up the loop in the subroutine? Do not give a description on an instruction-by instruction level; give the overall task of the loop. 

(v) Write a complete program to call the subroutine and test its functionality. The main program is to start at address 2000 (Hex) and the subroutine occupies memory space just below the main program.

Initialise and use test data: 1, 2, 3, ... up to the loop counter deduced in Question 4(b)(i). 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 pastes your program to your MS WORD answer document.
(9 marks)

(vi) Submit a screen shot of the memory contents that include addresses from 2E0 to 350 when the program stops. Use the instructions given below to obtain the screen shot.

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 ‘screen shot' select the window, press + on your computer keyboard, and then paste it onto your word document.