TI-92 Link Protocol Guide - Variable formats

A TI-92 variable has two parts: a header and a data section. While the header may be different, the format of the data section never changes whether the variable is in a file, in a transfer packet, or in the calculator's memory. This section describes the format of the data section for most types of variables. The format for the header is described in the packet format and the file format section.

Often certain variable types such as functions or lists are included in other larger variables. When such nesting occurs, it will be noted by referencing the type of subvariable rather than expanding its components. For example, a list contained in a GDB will be referenced as a list, not as the individual fields that make up a list.

Important note: All 2- and 4-byte values in this section are big-endian (MSB first) unless specified otherwise.

Variable Types

There are several types of variables that the TI-92 uses.

Expressions are basic algebraic expressions like the ones entered on the home screen.
Lists are sequences of real or complex numbers used in statistical calculations.
Matrices are two-dimensional matrices with real or complex components.
Data variables are spreadsheets containing values in some cells.
Text variables are files of readable text.
Strings are sequences of text characters.
Graphics Databases (GDB's) are stored sets of graphing functions.
Figures are objects created in the geometry application.
Pictures are stored bitmaps of the graph screen.
Programs are sequences of commands.
Functions are sequences of commands that evaluate based on the values of one or more variables.
Macros are stored command sequences for the geometry application.

Expressions

TI-92 expressions are tokenized and in Reverse Polish Notation (RPN). In RPN, each operand and each operator is a "symbol," which can be pushed onto a first-in-first-out (FIFO) "stack." A stack is a data structure that works like a stack of trays: new trays can be pushed onto the stack at any time, and trays on the stack can be popped off at any time, but they always come off in the reverse order than that in which they were pushed.

Operations are read from left to right. Whenever an operand is encountered, it is pushed onto the stack. Whenever an operator is encountered, it pops one or more operands off of the stack, uses them to compute the result, then pushes the result back onto the stack. The final value is the only operand left in the stack after all operations are complete. With this method, storing parenthesis is unnecessary because there are never any ambiguities as to the order of evaluation.

Click here for a list of tokens.

Offset	Length	Description
0	2 bytes	Number of bytes in this expression minus two for this field.
2	n bytes	Expression operands and operators, tokenized and in RPN.

Example - expression (a+b)*c:
00 05 0B 0C 8B 0D 8F
      a  b  +  c  *

Lists

A list is represented as an expression beginning with token E5h and ending with token D9h. The format of a list can be simplified as follows:

Offset	Length	Description
0	2 bytes	Number of bytes in this list minus two for this field
2	1 byte	This byte always contains E5h.
3	n bytes	Element values, one by one, last to first. Each element value is a NUMBER (a group of tokens, in Reverse Polish Notation, representing a single value).
3+n	1 byte	This byte always contains D9h.

Matrices

A matrix is represented as a list of row lists. The format can be simplified as follows:

Offset	Length	Description
0	2 bytes	Number of bytes in this list minus two for this field
1	1 byte	This byte always contains E5h.
3	n bytes	Rows, one by one, last to first. Each row is a List without the first two bytes.
3+n	1 byte	This byte always contains D9h.

Data variables

Data variables consist of a number of lists, functions and strings. They have the following format:

Offset	Length	Description
0	2 bytes	Number of bytes in this data variable minus two for this field
2	1 byte	The number of rows in the longest column
3	1 byte	The number of columns
4	n bytes	Column definitions, one by one, first to last. See format below.
4+n	1 byte	The number of column calculations
5+n	m bytes	Column calculation definitions, one by one, first to last. See format below.
5+n+m	1 byte	The number of column titles
6+n+m	x bytes	Column calculation definitions, one by one, first to last. See format below.
6+n+m+x	1 byte	This byte always contains DDh.

Each column definition follows this format:

Offset	Length	Description
0	1 byte	The column number (1-based)
1	y bytes	A List representing the column

Each column calculation definition follows this format:

Offset	Length	Description
0	1 byte	The column number (1-based)
1	y bytes	An Expression representing the calculation function

Each column title definition follows this format:

Offset	Length	Description
0	1 byte	The column number (1-based)
1	y bytes	A String representing the column title

Text variables

Text variables have the following format:

Offset	Length	Description
0	2 bytes	Number of bytes in this text variable minus two for this field
2	2 bytes	Offset, in characters, to the cursor position.
4	n bytes	Text lines (see format below)
4+n	1 byte	This byte always has a value of E0h.

Each line of text has this format:

Offset	Length	Description
0	1 byte	Line type: 0Ch=page break, 20h=normal, 43h=Command, 50h=PrintObj
1	m bytes	Characters, first to last. The string is not zero-terminated.
1+m	1 byte	Line delimiter: 0Dh=line break, 00h=end of file

Strings

Strings are represented as follows:

Offset	Length	Description
0	2 bytes	Number of bytes in this string minus two for this field
2	1 byte	This byte always has a value of 0.
3	n bytes	Characters, first to last. The string is zero-terminated.
3+n	1 byte	This byte always has a value of 2Dh.

Graphics Databases (GDB's)

GDB's for each graphing mode are different, but they all consist of a window setup portion and a function library portion.

All GDB have the following overall format:

Offset	Length	Description
0	2 bytes	Number of bytes in this GDB minus two for this field.
2	1 byte	Number of graphs (1 or 2)
3	1 byte	Angle mode: 01h=Radians, 02h=Degrees
4	1 byte	Complex number mode: 01=Real, 02=Rectangular, 03=Polar
5	1 byte	Graph mode: 01h=Function, 02h=Polar, 03h=Parametric, 04h=Sequence, 05h=3D
6	1 byte	Active graph number (0 or 1) - Not present when #graphs=1
7	1 byte	Graph 2 mode (same possible values as offset 3) - Not present when #graphs=1
8	1 byte	Split Screen mode: 01h=Full, 02h=Top/Bottom, 03h=Left/Right - Not present when #graphs=1
9	1 byte	Split Screen ratio: 01h=1:1, 02h=1:2, 03h=2:1 - Not present when #graphs=1
6 or 10 (Ah)	n bytes	One or two graphs back to back (see various graph formats below).
6+n or 10 (Ah)+n	1 byte	This byte always contains DEh.

Note: When two graphs of the same graph mode are included in one GDB, the second graph does not contain any function definitions.

A function-mode graph has this format:

Offset	Length	Description
0	10 bytes	A REAL: xmin (see REAL format, below)
10 (Ah)	10 bytes	A REAL: xmax
20 (14h)	10 bytes	A REAL: xscl
30 (1Eh)	10 bytes	A REAL: ymin
40 (28h)	10 bytes	A REAL: ymax
50 (32h)	10 bytes	A REAL: yscl
60 (3Ch)	10 bytes	A REAL: x
70 (46h)	10 bytes	A REAL: y
80 (50h)	10 bytes	A REAL: xres
90 (5Ah)	2 bytes	Graphing format flags (see graph format flags, below)
92 (5Ch)	2 bytes	Reserved; these bytes always have a value of 0h
94 (5Eh)	1 byte	The number of functions in this graph
95 (5Fh)	n bytes	Function definitions, one after another (see function definition format, below).
95 (5Fh)+n	1 byte	This byte always has a value of 0.
96 (60h)+n	1 byte	Table setup flags (see table setup flags, below).
97 (61h)+n	10 bytes	A REAL: tblStart
107 (6Bh)+n	10 bytes	A REAL: tbl
117 (75h)+n	x bytes	A List: tblInput

A polar-mode graph has the following format:

Offset	Length	Description
0	10 bytes	A REAL: xmin (see REAL format, below)
10 (Ah)	10 bytes	A REAL: xmax
20 (14h)	10 bytes	A REAL: xscl
30 (1Eh)	10 bytes	A REAL: ymin
40 (28h)	10 bytes	A REAL: ymax
50 (32h)	10 bytes	A REAL: yscl
60 (3Ch)	10 bytes	A REAL: x
70 (46h)	10 bytes	A REAL: y
80 (50h)	10 bytes	A REAL: min
90 (5Ah)	10 bytes	A REAL: max
100 (64h)	10 bytes	A REAL: step
110 (6Eh)	2 bytes	Graphing format flags (see graph format flags, below)
112 (70h)	2 bytes	Reserved; these bytes always have a value of 0h
114 (72h)	1 byte	The number of functions in this graph
115 (73h)	n bytes	Function definitions, one after another (see function definition format, below).
115 (73h)+n	1 byte	This byte always has a value of 0.
116 (74h)+n	1 byte	Table setup flags (see table setup flags, below).
117 (75h)+n	10 bytes	A REAL: tblStart
127 (7Fh)+n	10 bytes	A REAL: tbl
137 (89h)+n	x bytes	A List: tblInput

A parametric-mode graph has the following format:

Offset	Length	Description
0	10 bytes	A REAL: xmin (see REAL format, below)
10 (Ah)	10 bytes	A REAL: xmax
20 (14h)	10 bytes	A REAL: xscl
30 (1Eh)	10 bytes	A REAL: ymin
40 (28h)	10 bytes	A REAL: ymax
50 (32h)	10 bytes	A REAL: yscl
60 (3Ch)	10 bytes	A REAL: x
70 (46h)	10 bytes	A REAL: y
80 (50h)	10 bytes	A REAL: tmin
90 (5Ah)	10 bytes	A REAL: tmax
100 (64h)	10 bytes	A REAL: tstep
110 (6Eh)	2 bytes	Graphing format flags (see graph format flags, below)
112 (70h)	2 bytes	Reserved; these bytes always have a value of 0h
114 (72h)	1 byte	The number of functions in this graph
115 (73h)	n bytes	Function definitions, one after another (see parametric function definition format, below).
115 (73h)+n	1 byte	This byte always has a value of 0.
116 (74h)+n	1 byte	Table setup flags (see table setup flags, below).
117 (75h)+n	10 bytes	A REAL: tblStart
127 (7Fh)+n	10 bytes	A REAL: tbl
137 (89h)+n	x bytes	A List: tblInput

A sequence-mode graph has the following format:

Offset	Length	Description
0	10 bytes	A REAL: xmin (see REAL format, below)
10 (Ah)	10 bytes	A REAL: xmax
20 (14h)	10 bytes	A REAL: xscl
30 (1Eh)	10 bytes	A REAL: ymin
40 (28h)	10 bytes	A REAL: ymax
50 (32h)	10 bytes	A REAL: yscl
60 (3Ch)	10 bytes	A REAL: x
70 (46h)	10 bytes	A REAL: y
80 (50h)	10 bytes	A REAL: nmin
90 (5Ah)	10 bytes	A REAL: nmax
100 (64h)	10 bytes	A REAL: plotstrt
110 (6Eh)	10 bytes	A REAL: plotstep
120 (78h)	2 bytes	Graphing format flags (see graph format flags, below)
122 (7Ah)	1 byte	X Axis: FFh = n, 00h = u, otherwise i = ui(n).
123 (7Ah)	1 byte	Y Axis: FFh = n, 00h = u, otherwise i = ui(n).
124 (7Ch)	1 byte	The number of functions in this graph
125 (7Dh)	n bytes	Function definitions, one after another (see function definition format, below).
125 (7Dh)+n	1 byte	The number of initial values in this graph
126 (7Eh)+n	m bytes	Initial value definitions, one after another (see initial value definition fromat, below).
126 (7Eh)+n+m	1 byte	Table setup flags (see table setup flags, below).
127 (7Fh)+n+m	10 bytes	A REAL: tblStart
137 (89h)+n+m	10 bytes	A REAL: tbl
147 (93h)+n+m	x bytes	A List: tblInput

A 3D-mode graph has this format:

Offset	Length	Description
0	10 bytes	A REAL: xmin (see REAL format, below)
10 (Ah)	10 bytes	A REAL: xmax
20 (14h)	10 bytes	A REAL: xgrid
30 (1Eh)	10 bytes	A REAL: ymin
40 (28h)	10 bytes	A REAL: ymax
50 (32h)	10 bytes	A REAL: ygrid
60 (3Ch)	10 bytes	A REAL: x
70 (46h)	10 bytes	A REAL: y
80 (50h)	10 bytes	A REAL: zmin
90 (5Ah)	10 bytes	A REAL: zmax
100 (64h)	10 bytes	A REAL: zscl
110 (6Eh)	10 bytes	A REAL: eye°
120 (78h)	10 bytes	A REAL: eye°
130 (82h)	10 bytes	A REAL: An unnamed value dependent on eye° and the screen width
140 (8Ch)	10 bytes	A REAL: An unnamed value dependent on eye°, eye° and the screen height
150 (96h)	2 bytes	Graphing format flags (see graph format flags, below)
152 (98h)	2 bytes	Reserved; these bytes always contain 0.
154 (9Ah)	1 byte	The number of functions in this graph
155 (9Bh)	n bytes	Function definitions, one after another (see function definition format, below).
155 (9Bh)+n	1 byte	This byte is always 0.

The graph format flags word has the following format:

Bit (Mask)	Mode if set (1)	Mode if clear (0)
0 (0001h)	Coordinates: POLAR	Coordinates: RECT
1 (0002h)	Leading Cursor: ON	Leading Cursor: OFF
2 (0004h)	Labels: ON	Labels: OFF
3 (0008h)	Axes: BOX	Axes: AXES
4 (0010h)	Axes: OFF	Axes: ON
5 (0020h)	Grid: ON	Grid: OFF
6 (0040h)	Graph Order: SIMUL	Graph Order: SEQ
7 (0080h)	Coordinates: OFF	Coordinates: ON
8 (0100h)	Style: WIRE FRAME	Style: HIDDEN SURFACE
13 (2000h)	Build Web: AUTO	Build Web: TRACE
14 (4000h)	Axes: WEB	Axes: TIME or CUSTOM
15 (8000h)	Axes: TIME	Axes: WEB or CUSTOM

The table setup flags byte has the following format:

Bit (Mask)	Mode if set (1)	Mode if clear (0)
6 (0040h)	Independent: ASK	Independent: AUTO
7 (0080h)	Graph <-> Table: ON	Graph <-> Table: OFF

Function, polar, sequence and 3D-mode function definitions have the following format:

Offset	Length	Description
0	1 byte	Function ID (the number of the function).
1	n bytes	A Function yi(x), ri(), ui(n), or zi(x,y)

Parametric-mode function definitions have the following format:

Offset	Length	Description
0	1 byte	Function ID (the number of the function) with bit 7 clear.
1	n bytes	A Function xti(t)
1+n	1 byte	Function ID (the number of the function) with bit 7 set.
2+n	m bytes	A Function yti(t)

REAL values referred to in the above GDB format definitions are represented by a sign bit, a 15-bit binary number containing the base-10 exponent, and a binary-coded-decimal (4 bits per decimal digit) 16-digit mantissa:

Offset	Length	Description
0	1 byte	Sign bit (bit 7) and upper 7 bits of exponent (bits 0-6)
1	1 byte	Lower 8 bitts of exponent
2	8 bytes	BCD mantissa

Figures

There is no information available about this data type at this time.

Pictures

Pictures are 128x63-pixel bitmaps. They have the following format:

Offset	Length	Description
0	2 bytes	Number of bytes in this picture minus two for this field
2	2 bytes	Height, in pixels, of the picture.
4	2 bytes	Width, in pixels, of the picture.
6	n bytes	Monochrome (1 bpp) bitmap. (n = height * ceiling[width/8] )
6+n	1 byte	This byte always has a value of DFh.

The following figure demonstrates byte ordering of the pixels if the bitmap for a 128x63 picture is in a 1008-element array data[]:

Programs

Programs are represented as a series of tokens in Reverse Polish Notation enclosed in the Prgm and EndPrgm tokens. They can be either tokenized or untokenized.

Untokenized programs have this format:

Offset	Length	Description
0	2 bytes	Number of bytes in this program minus two for this field
2	n bytes	Zero-terminated ASCII text starting with the "(" character in the program name. Line breaks are represented as 0Dh bytes. The colon (":") characters after the line breaks are not stored.
2+n	2 bytes	Offset, in characters, of the cursor from the beginning of the program
4+n	3 bytes	These three bytes always contain {19h, E4h, E5h} (Endprgm and '}' tokens).
7+n	4 bytes	These four bytes always contain {00h, 00h, 08h, DCh}.

Tokenized programs have this format:

Offset	Length	Description
0	2 bytes	Number of bytes in this program minus two for this field
2	n bytes	Program tokens to be pushed onto the stack, then executed once complete.
2+n	4 bytes	These four bytes always contain {00h, 00h, 40h, DCh}.

The program tokens are generally in reverse order of execution, following the Reverse Polish Notation method that the TI-92 uses. The first tokens in execution order specify the arguments for the program. The next token is always E5h, followed by the "Prgm" token (E4h+19h), then the program statements. Following the program statements is the "EndPrgm" token (E4h+12h), then the E9h token. Each statement is separated by a 00h byte, and line breaks are represented as E8h tokens. Statements on the same line are separated by E7h tokens.

Click here for a table of token definitions.

Functions

The format for functions is similar to the format for programs. Functions can be but are not required to be enclosed in Func and Endfunc tokens. Functions, like programs, can be tokenized or untokenized.

Untokenized functions have this format:

Offset	Length	Description
0	2 bytes	Number of bytes in this function minus two for this field
2	n bytes	Zero-terminated ASCII text starting with the "(" character in the function name. Line breaks are represented as 0Dh bytes. The colon (":") characters after the line breaks are not stored.
2+n	2 bytes	Offset, in characters, of the cursor from the beginning of the function
4+n	3 bytes	These three bytes always contain {17h, E4h, E5h} (Endfunc and '}' tokens).
7+n	2 bytes	These two bytes always have a value of 0.
9+n	1 byte	Flags (see format below).
10 (Ah)+n	1 byte	This byte always contains DCh.

Tokenized functions have this format:

Offset	Length	Description
0	2 bytes	Number of bytes in this program minus two for this field
2	n bytes	Program tokens
7+n	2 bytes	These two bytes always have a value of 0.
9+n	1 byte	Flags (see format below).
10 (Ah)+n	1 byte	This byte always contains DCh.

The flags byte has the following format:

Bit (Mask)	Mode if set (1)	Mode if clear (0)
0 (01h)	Graph style: 000=line, 001=dot, 010=thick line, 011=animate, 100=path, 101=shade above, 110=shade below, 111=square
1 (02h)
2 (04h)
3 (08h)	Untokenized	Tokenized
4 (10h)	Unknown
5 (20h)	Unknown
6 (40h)	Graph 1 plot on	Graph 1 plot off
7 (80h)	Graph 2 plot on	Graph 2 plot off

Macros

There is no information available about this data type at this time.

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