em2.mp4

You can find the details of the tests either towards the end of the video or in the lower section of the application description.

COMMAND SYSTEM

A custom educational computer was developed based on the von Neumann architecture, with a set of instructions designed and implemented to enable input and output of data, perform arithmetic operations (addition, subtraction, multiplication, division, and remainder calculation), as well as other commands to transfer data between memory locations, among other functions. All instructions execute sequentially, except for conditional and unconditional branching instructions, which can modify the program flow. Each instruction takes two operands (memory addresses) as inputs, and for arithmetic instructions, the result is stored in a memory location specified by one of the operands. The computer's memory consists of 512 lines with addresses ranging from 1 to 512.

A table is provided below with the implemented instructions, their corresponding mnemonic codes, and a brief description of their functions:

№	COM	DESCRIPTION
0	TFR	Transferring value from A2 to A1
1	ADR	Addition of real numbers: A1 = A1 + A2
2	SBR	Subtraction of real numbers: A1 = A1 - A2
3	MLR	Multiplication of real numbers: A1 = A1 × A2
4	DVR	Division of real numbers: A1 = A1 ÷ A2
5	EAR	Entering an array of real numbers in quantity A2, starting from address A1
6	EAI	Entering an array of integers in the amount of A2, starting from the address A1
7	???	???
8	???	???
9	UNT	Unconditional transition from the current line to line A2
10	INT	Conversion of real number A1 to integer A2
11	ADI	Addition of integers: A1 = A1 + A2
12	SBI	Subtraction of integers: A1 = A1 - A2
13	MLI	Multiplication of integers: A1 = A1 × A2
14	DVI	Division of integers: A1 = A1 ÷ A2
15	OAR	Output of the array of real numbers in the quantity A2, starting from the address A1
16	OAI	Output of an array of integers in quantity A2, starting from address A1
17	???	???
18	CZT	Conditional transition: if the flag Z is 0 — transition to line A1, if the flag Z* is 1 — transition to line A2
19	CWT	Conditional transition: if the flag 𝜔 is 0 or 2 — transition to line A1, if flag 𝜔* is 1 — transition to line A2
20	REA	Conversion of an integer A1 into a real number A2
21	???	???
…	…	…
23	???	???
24	MOD	Remainder from division of integers
25	???	???
…	…	…
29	???	???
30	ITR	Move A2 (currently used array cell index) at address A1 to A2 elements
31	END	Completion of program execution

Table 1. Learning machine command system

REGISTERS AND FLAGS

The current instruction in the machine is executed using operands stored in registers, which are categorized as RK, R1, R2, and RA based on their logical interpretation. RK represents the current command, RA represents the address number of the current line, and R1 and R2 are the operands on which the instruction is executed.

The 𝜔 flag, also known as "omega," changes based on the result of arithmetic operations such as addition, subtraction, division, and multiplication. It is used for conditional transitions and has a value of 0 if the result of the operation is zero. If the result is less than zero, the flag is set to 1; if greater than zero, it is set to 2.

Other flags include S, which represents the result sign, C, which represents the sign of the transfer from the higher order, T, which is a step-by-step mode flag (for debugging), and Z, which represents a zero-result flag used in conditional transitions.

In case of an error during program execution, the Err flag is raised and its value changes from 0 to 1, causing the program to crash.

All registers and flags are accessible through the GUI form panel, providing complete information about the current command and its operands during machine execution in debug mode.

IMPLEMENTATION OF EDUCATIONAL MACHINE

TOOLS

The emulator for the two-address learning machine was developed using C# programming language and the Microsoft WPF .Net Framework, which is a framework for building graphical user interfaces for Windows operating systems. The project was created in the Microsoft Visual Studio 2022 integrated development environment.

GRAPHICAL USER INTERFACE

The graphical user interface (GUI) of the educational machine is designed to simplify its use. It includes several functional elements, which are numbered in the screenshot of the main window.

Picture 1. Graphical user interface

1. The program code table allows users to enter and edit commands for the learning machine. This table supports both integer and real numbers as inputs. If the user enters incorrect data, the diagnostics window will display an error message upon program start.
2. During program execution, the user may be prompted to enter data via a pop-up window. Users can enter integer or real numbers using the keyboard. If an incorrect value is entered or the user cancels the input operation, an error message will be displayed in the diagnostics window. Otherwise, the entered value will be displayed in the "Input" window.
3. The "Output" window displays the integer or real number generated by the program.
4. The registers and flags panel displays the current values of these components during program execution. In step-by-step mode, this panel provides a clear demonstration of the program execution process.
5. The "Diagnostics" window displays any warnings, remarks, or unexpected situations that may occur during program execution.
6. The panel displays the path to the open file.
7. The top of the window contains several auxiliary and control buttons, including "Save", "Save as", "Open", "Help", and "Cleaning". The "Run" button runs the program without debugging, the "Start debugging" button starts a step-by-step program run, the "Step" button goes to the next command, and the "Finish debugging" button ends the step-by-step program run.

Picture 2. Window for entering a real number

Picture 3. Help window

TRAINING MACHINE PROGRAMS

LINEAR CALCULATIONS

We will test the feasibility of linear calculations by compiling a program and running it on the emulator of the learning machine we have created. This will allow us to evaluate the implementation of arithmetic operations, including addition, subtraction, multiplication, and division.

Task #17: calculate the value of the function y = (4 * x^3 + 10 * z) / (x * z^2), the values of “x” and “z” are set by the user using input operations from the keyboard.

Below is the code of the corresponding program in the form of a table:

ADR	COM	A1	A2	DESCRIPTION
1	EAI	15	2	User input of “x” and “z” values in addresses 15 and 16
2	TFR	17	15	Forwarding “x” to the 17th address so as not to lose the value later
3	TFR	18	16	Forwarding “z” to 18 address so as not to lose the value later
4	MLR	17	15	Multiplying “x” by “x” (squaring)
5	MLR	17	15	Multiplying “x^2” by “x” (cubing)
6	MLR	14	17	Multiplication of “x^3” by 4, sent in advance to address 14
7	MLR	18	16	Multiplying “z” by “z” (squaring)
8	MLR	18	15	Multiplication of “z^2” by “x” (calculation of the divisor)
9	MLR	19	16	Multiplying “z” by 10, sent in advance to address 19
10	ADR	14	19	Addition of 4x3 and 10z (calculation of division)
11	DVR	14	18	Final division of pre-calculated values
12	OAR	14	1	Output of the calculated result of the function
13	END	000	000	Stopping program execution
14	TFR	000	4	Forwarding to 14 address 4
…	…	…	…	…
19	TFR	000	10	Forwarding to 19 address 10

Table 2. Linear expression calculation program code

CALCULATION USING CYCLES

In order to explore the potential of implementing cyclic calculations, we will develop a program that utilizes loops and control structures. This program will be compiled and executed using the newly created learning machine emulator. By doing so, we can assess the emulator's ability to handle iterative computations and further validate its capabilities.

Task #2: calculate the value of the expression (wolfram alpha math input) y = Product[i^3 / (a - b), {i, 1, n}] with the values “a” and “b” specified by the user, if a != b, or calculate the value of the expression (a - b) / (a + b) if a = b.

Below is the code of the corresponding program in the form of a table:

ADR	COM	A1	A2	DESCRIPTION
1	EAR	40	3	User input of values “a”, “b” and “i” in addresses 40, 41 and 42
2	TFR	50	40	Forwarding “a” to 50 address so as not to lose the value later
3	TFR	51	41	Forwarding “b” to 51 address so as not to lose the value later
4	SBR	40	41	Checking whether a - b is zero (creating a null result flag)
5	CZT	8	6	If the flag is now 0 (the result of the operation was not equal to 0), then go to address 8, otherwise - to 6
6	UNT	000	20	Unconditional transition to the 20th address for further calculation of the result
7	END	000	000	Stopping program execution
8	SBR	42	55	We check whether the iterator (stored in address 55) is not greater than the number of iterations required by the user (stored in address 42). We form the flag 𝜔: if the subtraction result is greater than or equal to 0, then 𝜔 = 2 (0), otherwise 𝜔 = 1
9	CWT	10	18	If the calculated flag 𝜔 is equal to 0 or 2, then we go to address 10, otherwise (equal to 1) to 18
10	ADR	42	55	We return the number of iterations required by the user to the initial value (before the formation of 𝜔)
11	TFR	57	55	Forwarding the iterator value to address 57 so as not to lose the value
12	MLR	57	55	Multiplying “i” by “i” (squaring)
13	MLR	57	55	Multiplying “i2” by “i” (cubing)
14	DVR	57	40	Division of i3 by the previously calculated difference a - b
15	MLR	512	57	Multiply the result by the just calculated value
16	ADR	55	56	We increase the iterator by one
17	UNT	000	8	Unconditional jump to address 8 to continue (or end) the cycle
18	OAR	512	1	Display the calculation result on the screen
19	END	000	000	Stopping program execution
20	ADR	50	51	Since a - b has already been calculated in address 4 (the result is 40), it remains to calculate only the sum
21	DVR	40	50	We divide the difference a - b by the just calculated sum a + b
22	OAR	40	1	We display the calculation result on the screen
23	UNT	000	7	Go to address 7 to complete the program
…	…	…	….	…
55	TFR	000	1	Forwarding to 55 address 1
56	TFR	000	1	Forwarding to 56 address 1
…	…	…	…	…
511	TFR	000	0	Forwarding to 511 address 0, to calculate the amount
512	TFR	000	1	Forwarding to 512 address 1, to calculate the product

Table 3. The code of the program for calculating an expression using loops

CALCULATIONS USING CYCLES (ARRAYS)

In order to assess the potential of the learning machine emulator for implementing array calculations using loops, we will compile a program and subsequently launch it using the emulator. This program will serve as a test case to evaluate the accuracy and efficiency of the emulator when executing array calculations through the use of loops.

Task No. 11: Compile a program for counting in an integer array the number of zero elements after the element with the number specified by the user.

Below is the code of the corresponding program in the form of a table:

ADR	COM	A1	A2	DESCRIPTION
1	EAI	100	5	Filling by the user of an array of 5 elements, starting from 100 address
2	EAI	105	1	The user enters the index of the array, starting from which the calculation of the result will take place at address 105
3	SBI	105	30	Checking whether the iterator (at address 30) has reached the initial value (entered by the user at address 105) to start calculations. Formation of the null result flag
4	CZT	7	5	Conditional transition: if the iterator has not yet reached the initial index (flag equals 0), transition to address 7, otherwise (flag 1) to address 5
5	ADI	105	30	We return the initial index to its starting value (which changed after executing the code at address 3)
6	UNT	000	11	Unconditional transition to the 11th address
7	ADI	105	30	We return the initial index to its starting value (which changed after executing the code at address 3)
8	ADI	30	31	The iterator has not yet reached the initial index, we increase it by one
9	ITR	14	1	We shift the address (A1) of the required array cell in address 14 by one
10	UNT	000	3	Unconditional transition to the 3rd address
11	SBI	32	30	We check whether the iterator (stored in address 30) is not greater than the number of elements of the array (stored in address 32)
12	CWT	13	22	If the value of the flag 𝜔 is equal to 0 (or 2), then we continue the cycle and go to address 13, otherwise (𝜔 is equal to 1) to address 22
13	ADI	32	30	We return the initial number of elements of the array to its starting value (which changed after executing the code at address 11)
14	ADI	100	34	I add a zero to the current element of the array (which changes to 1 after executing the code at address 9 and 15). Forming a zero result flag: if the element of the array was zero, then the flag will be equal to 1, otherwise 0
15	ITR	14	1	We shift the address (A1) of the required array cell in address 14 by one
16	CZT	17	19	Conditional transition: if the null result flag is 0 to address 17, otherwise (the flag is 1) to address 19
17	ADI	30	31	I increase the iterator by one
18	UNT	000	11	Unconditional transition to address 11
19	ADI	30	31	I increase the iterator by one
20	ADI	33	31	I increase the number of zeros in the array by one (initially 0 is stored at address 33)
21	UNT	000	11	Unconditional transition to address 11
22	OAI	33	11	Output of the number of zeros on the screen
23	END	000	000	Stopping program execution
…	…	…	…	…
30	TFR	000	1	Forwarding to 30 addresses 1
31	TFR	000	1	Forwarding to 31 address 1
32	TFR	000	5	Forwarding to 32 address 5

Table 4. Code of the program for calculating arrays using loops

If you have any difficulties while using the emulator, please don't hesitate to contact me at https://t.me/worriedsick or via email at tymofii.striukov@gmail.com. I'll be more than happy to assist you with any questions or concerns you may have.