Computer Organization and Design

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Problem 1：

Convert the following decimal values to both binary and hexadecimal representations using 8 bit two’s complement. If you cannot convert to twos complement please explain why.

2310= 00010111_two=17_hex

-1510= 11110001_two=F1_hex

-12810= 10000000_two=80_hex

12810: 关于 2’s complement，8 bit可以表示的数值范围只有【-128，+127】；故128无法用8 bit2’s complement 表示;

-110= 11111111_two=FF_hex

Problem 2:

Convert the following LC2K assembly code into machine code in hex. All unused bits should be 0 and the machine code instructions should be 32 bits long.

add        1  2  3                           ： 0x000A0003

start       lw           4  5  ten                        ： 0x00A50004

beq        3  5  start                       ： 0x011DFFFE

halt                                             ： 0x01800000

ten         .fill          10                                ： 0x0000000A

Problem 3: 

Convert the following hex numbers to LC2K instructions.

0x00550003                     : nand  2  5  3

0x01670000                      : jalr 4   7

0x00CAFFFF                      : sw    1   2   -1

Problem 4: 

Given the following MIPS assembly code (and assuming all registers start at 0):

addi   $1    $0    3

addi   $2    $0    8

loop   add   $1    $1    $2

nand  $3    $1    $2

addi   $2    $2    -2

bne   $0    $2    loop

a) Translate the MIPS code into C Code that performs the same operations. Please use the variable names reg1, reg2, and reg3 for $1, $2, and $3.

int reg1, reg2, reg3;

reg1 = 3;

reg2 = 8;

do

{

reg1 = reg1+reg2;

reg3 = ~(reg1&reg2);

reg2 = reg2+(-2);

}

while (reg2 !=0);

b) How many times is the line, “nand $3, $1, $2” executed?

4 times;

c) What is the final value of $3?

-3₁₀;

Problem 5: 

Below is the description of a new, stack-based ISA that only contains one register, REG. The ISA is byte addressable.

R-type Instructions            bits 7-5: opcode

bits 4-0: unused

I-type Instructions   bits 7-5: opcode

bits 4-0: immediate value in 2’s complement form

U-type Instructions           bits 7-5: opcode

bits 4-2: unused

bits 1-0: math code

a) Translate the following instructions into machine code. Please write your answers in HEX.

b) You are given the following C code that you are to translate into this ISA’s assembly.

a = b nand c

Assume that the stack is NOT initially empty and STACK[bottom] = 0.

a is located at memory address 10, b is at 20, c is at 30. REG is initially 0. Write your code below.

load         20

push

load         30

ALU.Nand

store       10