CSE306 Homework 3

CSE306 Processing Systems and Structures Lockwood, Spring 2004

Homework Assignment 3

Due: Monday Mar. 22, 2004, 5:30pm

75 Points

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Representing Floating Point Numbers

Suppose that we wish to represent floating point numbers using a 1-bit sign, a 4-bit exponent with a bias of 7, and an 8-bit mantissa with an implict 1. Determine the floating point representation for each of the following numbers.

Round mantissas to the nearest digit if necessary
Use IEEE-754 notation to represent special numbers.
Enter all values in binary (1's and 0's)

Number = 5.0

Sign = (1 pt)

Exponent = (1 pt)

Mantissa = (1 pt)

Number = 1.0

Sign = (1 pt)

Exponent = (1 pt)

Mantissa = (1 pt)

Number = -1.125

Sign = (1 pt)

Exponent = (1 pt)

Mantissa = (1 pt)

Number = -113.6

Sign = (1 pt)

Exponent = (1 pt)

Mantissa = (1 pt)

Electronic charge of an electron, measured in Coulombs.

Sign = (1 pt)

Exponent = (1 pt)

Mantissa = (1 pt)

Calculations with the Floating Point Unit

Determine the how the floating point variables will change for the code listed below

; Excepts from Explorer-3D ; John Lockwood ; 1998 ... Vector3 STRUCT ; Use Structure to grouping several variables X Real4 ? ; into one entity. They are the basis for classes in C++ Y Real4 ? Z Real4 ? Vector3 ENDS ... Position Vector3<12.5,25.0,100.0> ; Initial position Vector Velocity Vector3<10.0,20.0,30.0> ; Initial velocity OldX Real4 ? OldXR8 Real8 ? XMove Real4 ? ZMove Real4 1000.0 DeltaT Real10 0.125 ; 1/8th of a second MoveAngle Real10 3.0 WallHeight DW 5 ; Height of Maze walls (Integer distance in meter) FloorHeight DW 20 ; Height of Maze walls (Integer distance in meter) ... FINIT ; Initialize the FPU ; Always do this once when program begins! FLD Position.X ; Access element of the Vector3 Structure FST OldX ; Save Position.X FST OldXR8 ; Also save as Double-precision FLD Velocity.X FLD DeltaT FMUL FST XMove FADD FSTP Position.X LEA SI , Position ; Load effective address of Position FLD (Vector3 PTR [SI]).Y ; Cast [SI] as a pointer to a Vector3 FILD FloorHeight ; Load an Integer into FPU FILD WallHeight FSUB FADD FST (Vector3 PTR [SI]).Y FSTP (Vector3 PTR [SI+4]).Y ; The '+4' is important.. XOR BYTE PTR [Velocity.X+3] , 80h ; FCHS w/o a FPU! MOV AX,DS ; Set ES=DS MOV ES,AX LEA SI , Velocity.Y ; All variables can be moved in Memory LEA DI , Velocity.Z MOVSD FLD ZMove FLDPI FLD MoveAngle FDIV FCOS ; FPU Calculates on Radians FMUL FSTP ZMove

OldX = (8 hex digits) (3 pts)

OldXR8 = (16 hex digits) (3 pts)

XMove = (8 hex digits) (3 pts)

Position.X = (8 hex digits) (3 pts)

Position.Y = (8 hex digits) (3 pts)

Position.Z = (8 hex digits) (3 pts)

Velocity.X = (8 hex digits) (3 pts)

Velocity.Z = (8 hex digits) (3 pts)

ZMove = (8 hex digits) (3 pts)

Text-Mode Video

For each of the elements that we wish to display on an 80x25 text-mode screen, determine the attribute (AH), character (AL), and offset (DI) into video memory that must be established before we execute the following code:
Specify all numbers in hex.

The letter 'C' in blue on a black background at row 0, column 4.

AX= (2 pts)

DI= (2 pts)

The letter 'S' in (intense) white on a green background at row 3, column 3.

AX= (2 pts)

DI= (2 pts)

A magenta (purple) heart on a black background at row 10, column 54.

AX= (2 pts)

DI= (2 pts)

An intensely-colored green clover on a black background on the third text-mode video page (page 2) at row 2, column 3.

AX= (2 pts)

DI= (2 pts)

A blinking, empty, black, smiley character on a purple (red+blue) background on the fourth text-mode video page (page 3), at the lower-righthand corner of the screen.

AX= (2 pts)

DI= (2 pts)

Table-Lookup Functions

Consider the following code that uses a table-lookup function to efficiently encode and decode top-secret messages.

After running the program, OutputString =

(13 pts)

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