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TOPIC -- Apple II -- IA Floating point article

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Interface Age, November 1976, pages 103-111.

Floating Point Routines for the 6502*

by Roy Rankin

Department of Mechanical Engineering, Stanford University

and Steve Wozniak

Apple Computer Company

*First appeared in Dr. DOBB's Journal of Computer Calisthenics & Orthodontia, Box 310, Menlo Park, CA 94025

The following floating point routines represent a joint effort between Steve Wozniak who wrote the basic float- ing point routines of FADD, FSUB, FMUL, FDIV and their support routines and myself, Roy Rankin, who added FIX, FLOAT, LOG, LOG10, and EXP. The basic floating point routines are failry Machine dependent, but the transcendental programs should be very easy to transport from one machine to another. The routines consist of the following math functions

* LOG

Natural log

* LOG10

Base 10 log

* EXP

Exponential

* FADD

Floating add

* FSUB

Floating subtraction

* FMUL

Floating multiplication

* FDIV

Floating division

* FIX

Convert floating to fixed

* FLOAT

Convert fixed to floating

Two additional routines exchange the contents of exp/mant1 with exp/mant2 and compliments exp/

mant1. These routines

are

SWAP

 

Exchange

the contents of exp/mant 1 with

 

 

exp/mant

2

FCOMPL

Compliment exp/mant 1

Floating point numbers

are represented by 4 bytes as

shown in the following

 

+- SIGN BIT

+-

SIGN BIT

0 = +

0

= +

1 = -

1

= -

v

 

v

 

 

 

S

 

S

+-

PRESUMED DECIMAL POINT

B

 

B

v

 

 

__ _ _ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Page 91
Image 91
Apple II manual Log, Fadd, Fsub, Fmul, Fdiv, Fix, Fcompl, +- Sign BIT, Presumed Decimal Point

II specifications

The Apple II, launched in April 1977, was one of the first highly successful mass-produced microcomputer products. It marked a significant leap in personal computing, setting standards for future developments in the industry. Created by Steve Wozniak and Steve Jobs, the Apple II differentiated itself with its user-friendly design, appealing aesthetics, and robust capabilities.

One of the standout features of the Apple II was its open architecture, which allowed users to expand and enhance the computer's functionality. This design enabled hundreds of third-party hardware and software developers to contribute to its ecosystem, resulting in an array of peripherals, including printers, modems, and storage devices. The Apple II utilized a MOS Technology 6502 microprocessor running at a clock speed of 1 MHz. Initially equipped with 4 KB of RAM, the machine could be expanded to 48 KB, accommodating more complex applications and programs.

The Apple II was also notable for its colorful graphics. It was one of the first computers to support color display, offering a 6-color palette with a resolution of 280x192 pixels in 16 colors when using its Color Graphics Card. This feature significantly enhanced the visual appeal of games and educational software developed for the platform, making computing more accessible and entertaining for various audiences.

Apple's commitment to user experience was evident in the design of the machine. It featured an integrated keyboard and a plastic case, which was both durable and visually appealing. The self-contained design included drive bays for floppy disk drives, allowing for quicker data access than traditional tape drives. It also supported audio output, enabling sound effects and music, a novelty at the time.

The introduction of the Apple DOS operating system further underscored the machine's capabilities. DOS streamlined file management and made it easier for users to navigate and manage their data. The combination of hardware and software positioned the Apple II as an educational tool and a gaming platform, fostering a vibrant software ecosystem.

The Apple II family continued to evolve, with variations like the Apple II+, IIe, and IIgs being introduced over the years. These iterations brought enhancements in memory, processing power, and graphics capabilities. The legacy of the Apple II endures, not only as a foundational product in personal computing but also as a symbol of innovation that paved the way for future advancements in technology. Its impact is still felt today, as it inspired countless developers and shaped the trajectory of the computer industry.