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TI-86
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| Type | Graphing calculator |
|---|---|
| Manufacturer | Texas Instruments |
| Introduced | 1996 |
| Discontinued | 2006 |
| Latest firmware | 1.6 |
| Predecessor | TI-85 |
| Calculator | |
| Entry mode | D.A.L. |
| Display size | 128×64 pixels, 21×8 characters |
| CPU | |
| Processor | Zilog Z80 |
| Frequency | 6 MHz |
| Programming | |
| User memory | 96 kB of RAM |
| Other | |
| Power supply | 4 AAA's, 1 CR1616 or CR1620 |
The TI-86 is a programmable graphing calculator introduced in 1996 which was produced by Texas Instruments. The TI-86 uses the Zilog Z80 microprocessor. It is partially backwards-compatible with its predecessor, the TI-85.
In addition to having a larger screen than the TI-83, the TI-86 also allows the user to type in lower case and Greek letters and features five softkeys, which improve menu navigation and can be programmed by the user for quick access to common operations such as decimal-to-fraction conversion. The calculator also handles vectors, matrices and complex numbers better than the TI-83. One drawback, however, is that the statistics package on the TI-83 range doesn't come preloaded on the TI-86. However, it can be downloaded from the Texas Instruments program archive and installed on the calculator using the link cable.[1]
The TI-86 has been discontinued.[2]
Specifications
[edit]- CPU: Zilog Z80[3] 6 MHz
- RAM: 128 KB, 96 KB user-accessible
- ROM: 256 KB non-upgradable
- Display: 128×64 pixels high-contrast monochrome LCD
- Data Communication: Serial link port; allows two TI-86 calculators to be connected to each other, or one TI-86 to be connected to a PC, for data transfer via a special link cable
- Programming Languages: TI-BASIC, Z80 Assembly language (ASM)
- Power: 4×AAA, 1×CR1616 or CR1620 (for backup power)
See also
[edit]References
[edit]- ^ [1][dead link] (archived)
- ^ "TI-86 Features Summary". Archived from the original on November 18, 2008.
- ^ Campbell, Robert (2001). "TI-82/83/85/86 Mathematics Use". UMBC.
External links
[edit]- Official Texas Instruments TI-86 page (Internet Archive)
- ticalc.org hosts a large collection of downloadable freeware programs for the TI-86 can be found at along with programming tutorials and hardware extensions
- CalcG.org - Very organized and large archive of games and programs.
- The Guide - the largest set of tutorials for TI-86 assembly programming
- Texas Instruments Program Archive[dead link] (archived)
- Complete Disassembly of a TI-86
TI-86
View on GrokipediaDevelopment and Release
Background and Development
The TI-85, released by Texas Instruments in March 1992, marked the company's entry into advanced graphing calculators with support for assembly language programming, enabling users to create more sophisticated programs beyond basic keystroke operations.[4] This model targeted engineering and calculus applications but was constrained by 28 KB of RAM and an uppercase-only character set, limiting its handling of complex data and text-based inputs.[4] Development of the TI-86 began in the mid-1990s within Texas Instruments' education products division, building directly on the TI-85 to address these shortcomings while expanding capabilities for advanced high school and college mathematics.[5] Key goals included boosting programmability with native assembly language execution—unlike the TI-85's reliance on programming loopholes—increasing memory to 96 KB for more demanding operations, and introducing lowercase and Greek letters to improve the user interface for technical notation in engineering and calculus contexts.[5][6] These enhancements positioned the TI-86 as a mid-range tool without a computer algebra system (CAS), helping maintain affordability relative to higher-end models like the forthcoming TI-89, which incorporated CAS for symbolic manipulation.[7] Innovations during development emphasized core mathematical features, such as expanded matrix handling up to 80x80 dimensions (compared to the TI-85's 30x30 limit), integrated vector operations, and built-in complex number support represented as ordered pairs for easier computation in polar and rectangular forms.[1][8] The calculator retained the Zilog Z80-compatible processor architecture of its predecessor but incorporated a Toshiba T6A43 variant with additional ASIC integration for refined performance in graphing up to 99 functions and managing larger datasets.[1] Announced on January 6, 1997, and available in May of that year, the TI-86 reflected TI's focus on practical upgrades to meet evolving educational needs in a competitive market dominated by graphing calculators from rivals like HP and Casio.[1]Launch and Revisions
The TI-86 graphing calculator was introduced on January 6, 1997, and became commercially available starting in May 1997.[1] It was initially priced at $150 USD and targeted primarily at educational users in North American and European markets.[1] Production continued through 2008, when Texas Instruments officially discontinued the model on June 8.[1] Hardware revisions were limited to minor changes aimed at cost reduction and manufacturing efficiency.[9] Unlike the TI-83 series, which saw multiple major variants, the TI-86 had no significant hardware variants beyond a specialized teacher edition known as the TI-86 ViewScreen (VSC), which included a dedicated port for connecting to overhead projection panels.[10] The calculator shipped with operating system (OS) version 1.2 and received firmware updates up to version 1.6, which included bug fixes and enhancements such as improved matrix operations.[6] These updates were delivered via a serial connection to a personal computer using TI Graph Link software.[11] The TI-86 maintained full backwards compatibility with TI-85 programs and data, enabling TI-BASIC programs to be transferred and executed after conversion via computer if needed.[12]Design and Hardware
Physical Design
The TI-86 graphing calculator features a compact and portable form factor, measuring 1.0 × 3.5 × 7.3 inches (2.5 × 8.9 × 18.5 cm) and weighing 0.8 pounds (363 g), constructed from durable plastic in a black color scheme that resists everyday wear in educational settings.[2][13] This design prioritizes portability while maintaining robustness, with a contoured shape optimized for comfortable one-handed use during extended sessions of calculation or graphing. A slide-on protective cover is included to shield the device from scratches and impacts during transport.[14] The display is a monochrome LCD with a resolution of 128 × 64 pixels, offering a viewing area equivalent to 8 lines by 21 characters, which supports clear rendering of text, mathematical expressions, graphs, and multi-level menus.[15][16] Contrast is user-adjustable across 40 levels (0–9 via key combinations) to optimize visibility in various lighting conditions, though the screen lacks backlighting for power efficiency. This setup provides a larger viewing area than the contemporaneous TI-83's 96 × 64 pixel display, facilitating more detailed on-screen information without compromising readability.[15][14] The keyboard layout includes 47 keys arranged for intuitive access, encompassing alphanumeric characters, mathematical operations, four directional arrow keys for navigation, and dedicated keys for graphing (GRAPH) and mode selection (MODE).[15] Positioned directly below the display are five programmable softkeys (F1–F5), which dynamically change labels to offer context-sensitive menu options, streamlining user interaction with functions like variable access or editing tools.[15] The keys feature multi-layered labeling—primary white, secondary yellow via 2nd function, and tertiary blue via ALPHA—for efficient input of complex expressions.[15] Power is supplied by four AAA alkaline batteries, which provide reliable operation for typical student use, supplemented by a CR1616 lithium backup battery that preserves memory contents even when main batteries are depleted.[15] The device includes an automatic power-down feature after approximately 4 minutes of inactivity to conserve energy, and a low-battery indicator prompts replacement to avoid data loss.[15] Connectivity is handled via a 3-pin serial link port located on the bottom edge, enabling data transfer between TI-86 units, compatibility with TI-85 calculators, or linkage to computers using the optional TI-GRAPH LINK cable; USB support is absent, reflecting the era's technology standards.[15][17]Internal Components
The TI-86 utilizes a custom Toshiba T6A43 application-specific integrated circuit (ASIC) as its central processor, incorporating an 8-bit Z80-compatible microprocessor core clocked at 6 MHz. This design enables efficient real-time calculations and supports assembly-language programming, with the core featuring CMOS technology for low power operation and additional logic for handling interrupts and bus arbitration. The ASIC also integrates peripheral functions, such as keypad scanning and LCD timing control, reducing the overall component count on the board.[10][18] Memory in the TI-86 comprises 128 KB of static RAM (SRAM), of which 96 KB is accessible to users for storing programs, variables, and data, while the remaining portion is reserved for system operations. The read-only memory (ROM) totals 256 KB, housing the operating system and built-in applications in a non-upgradable format, though early production units allowed limited firmware updates via one-time programmable (OTP) ROM chips like the Atmel AT27C020 before transitioning to mask ROM variants such as the Sharp LH532. All storage relies on volatile RAM backed by battery power, with no provisions for flash memory or expansion card slots, limiting data persistence to battery life and available user memory for up to several hundred programs depending on size.[19][20][10] Supporting electronics include dedicated display drivers within the T6A43 ASIC for the 128×64 pixel LCD, supplemented by separate Toshiba T6A23 column driver and T6A40 row driver ICs to manage the high-contrast monochrome screen. A built-in serial port controller facilitates inter-device communication and connectivity to peripherals like the Calculator-Based Laboratory (CBL) system at 9600 baud. The overall architecture prioritizes battery efficiency through low-power CMOS components and minimal external circuitry.[18][10] The TI-86's printed circuit board (PCB) integrates these elements across two layers—one for main electronics and one for the display—with just five primary ICs: the T6A43 processor/ASIC, ROM chip, SRAM module (Epson SRM20100), and the two display drivers. Production occurred in Texas Instruments' facilities in Asia, such as Taiwan, during the late 1990s peak, with manufacturing dates like November 1997 noted on early units.[10]Features and Capabilities
Mathematical and Graphing Functions
The TI-86 graphing calculator supports a comprehensive set of basic mathematical operations, including real and complex arithmetic, trigonometric functions (such as sin, cos, and tan with their inverses), logarithmic functions (ln and log), and hyperbolic functions (sinh, cosh, and tanh with inverses).[15] These operations handle complex numbers in both rectangular and polar forms, with built-in functions like abs, angle, real, and imag for manipulation.[15] All computations use up to 14 digits of internal precision, though the display shows up to 12 digits plus a 3-digit exponent, with adjustable fixed or floating decimal places.[15] Graphing capabilities on the TI-86 allow plotting up to 99 functions simultaneously across various modes, including function (y(x)), parametric (xt(t), yt(t)), polar (r(θ)), and sequence graphing.[15] It supports simultaneous display of rectangular and polar graphs, enabling comparison of coordinate systems in a single view.[15] Users can generate function value tables with automatic or manual stepping via independent or ask-table settings, facilitating evaluation at specific points.[15] Graph analysis tools include trace mode for cursor navigation along plots to read coordinates, and zoom features such as box, standard, trigonometric, and fit-to-screen options for detailed inspection.[15] Conic sections can be graphed by entering their equations in the appropriate mode, such as parametric forms for ellipses or hyperbolas.[15] Advanced mathematical functions include numerical polynomial root finding up to 30th degree using the polyRoots or ROOT commands, which support real and complex solutions.[15] Numerical derivatives are computed via nDeriv for first-order and der2 for second-order approximations at specified points, without symbolic differentiation.[15] Integration is performed numerically with the fnInt command over definite intervals, employing an adaptive iteration method that refines estimates by doubling sample points.[15] Built-in statistical functions cover regressions such as linear, quadratic, exponential, and power models, but advanced statistical tools require separate download and installation.[21] The equation solver handles single or systems of up to 30 equations interactively, iterating to find roots within user-defined bounds and tolerances.[15] Unlike higher-end models, the TI-86 lacks symbolic manipulation capabilities for algebraic simplification or exact integration.[7]Data Handling and Analysis
The TI-86 graphing calculator provides built-in tools for managing structured data sets, enabling users to handle lists, matrices, vectors, and perform statistical computations efficiently. These features support educational applications in mathematics and science by allowing data entry, manipulation, and analysis directly on the device.[15] List management on the TI-86 allows for up to 99 lists, each containing a maximum of 999 elements, facilitating the organization of numerical data. Users can create lists using curly brace syntax, such as{1,2,3}, or through the dedicated List Editor for interactive entry and modification. Editing capabilities include inserting, deleting, or replacing elements, while sorting functions like sortA( for ascending order and sortD( for descending order help organize data quickly. Statistical summaries are accessible via functions such as mean( for the arithmetic mean, median( for the median, and stdDev( for standard deviation, providing essential descriptive statistics without external software.[15]
Matrix operations extend data handling to multidimensional arrays, supporting matrices from 1×1 up to 99×99 in size, limited by available memory. Basic arithmetic operations, including addition, subtraction, scalar multiplication, and matrix multiplication, are performed using standard operators, while advanced functions enable inversion of square matrices via the ^-1 operator and computation of determinants with det(. Row reduction is handled by ref( for row-echelon form and rref( for reduced row-echelon form, useful for solving systems of equations. The calculator also accommodates complex numbers within matrices, broadening applicability to engineering contexts.[15]
Vector handling focuses on 2D and 3D vectors, treated as special cases of lists or matrices with 2 or 3 elements. Operations include the dot product via dot( and the cross product via cross( for 3D vectors, along with magnitude calculation using norm(, which computes the Euclidean norm. These tools support vector algebra in physics and geometry without requiring custom programming.[15]
Statistical analysis capabilities emphasize one- and two-variable statistics, accessed through the 1-Var Stats and 2-Var Stats commands in the STAT menu, which compute measures like mean, median, standard deviation, and regression coefficients from list data. Advanced hypothesis testing, including t-tests for means and chi-square tests for goodness-of-fit (via TTEST or X2TEST options, with results stored in variables such as xStat and yStat), is available through the downloadable "Inferential Statistics and Distribution Functions" application.[22] While analysis of variance (ANOVA) is not built-in, it can be implemented through user programs. These functions prioritize core inferential statistics for classroom use.[15]
Data import and export occur primarily via the unit-to-unit link port, allowing transfer of lists and matrices between TI-86 calculators or compatible devices like the CBL system using the Send( and Get( functions in the LINK menu. For PC integration, TI Connect software enables bidirectional transfer of data variables, including importing numeric data from text files (.txt) into lists or matrices and exporting calculator data to editable formats on the computer. This facilitates workflow between handheld analysis and desktop processing.[15][23]