## Mc0071 Solved Assignments

### Quick-Start Guide

The calculator uses cross multiplication to convert proportions into equations which are then solved using ordinary equation solving methods. Be sure to enter something in each input box before clicking solve. Use the following as a guide:

#### Variables

Any lowercase letter may be used as a variable.

#### Exponents

Exponents are supported on variables using the ^ (caret) symbol. For example, to express x^{2}, enter x^2. Note: exponents must be positive integers, no negatives, decimals, or variables. Exponents may not be placed on numbers, brackets, or parentheses.

#### Parentheses and Brackets

Parentheses ( ) and brackets [ ] may be used to group terms as in a standard equation or expression.

#### Multiplication, Addition, and Subtraction

For addition and subtraction, use the standard + and - symbols respectively. For multiplication, use the * symbol. A * symbol is not necessiary when multiplying a number by a variable. For instance: 2 * x can also be entered as 2x. Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5). The * is also optional when multiplying parentheses, example: (x + 1)(x - 1).

#### Order of Operations

The calculator follows the standard order of operations taught by most algebra books - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The only exception is that division is not supported; attempts to use the / symbol will result in an error.

#### Division, Square Root, Radicals, Fractions

The above features are not supported.

#### Special Note

If either side of the proportion has a numerator and denominator that share a common factor with a variable, the calculator will report an erroneous solution. Example: 1/2 = x/x will cause the calculator to report 0 as a solution, even though there is no solution.

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#### Bigg Boss

__Control models:__

The models for structuring a system are concerned with how a system is decomposed into sub-systems. To work as a system, sub-systems must be controlled so that their services are delivered to the right place at the right time. Structural models do not (and should not) include control information. Rather, the architect should organize the sub-systems according to some control model, which supplements the structure model is used. Control models at the architectural level are concerned with the control flow between sub-systems.

Two general approaches to control can be identified:

(1) **Centralized control:** One sub-system has overall responsibility for control and starts and stops other sub-systems. It may also devolve control to another sub-system but will expect to have this control responsibility returned to it.

(2) **Event-based control:** Rather than control information being embedded in a sub-system, each sub-system can respond to externally generated events. These events might come from other sub-systems or from the environment of the system.

Control models supplement structural models. All the above structural models may be implemented using either centralized or event-based control.

**Centralized control**

In a centralized control model, one sub-system is designated as the system controller and has responsibility for managing the execution of other sub-systems.

**Event-driven systems**

In centralized control models, control decisions are usually determined by the values of some system state variables. By contrast, event-

driven control models are driven by externally generated events.

The distinction between an event and a simple input is that the timing of the event is outside the control of the process which handless that event.

A sub-system may need to access state information to handle these events but this state information does not usually determine the flow of control.

There are two event-driven control models:

(1) **Broadcast models:** In these models, an event is, in principle, broadcast to all sub-systems. Any sub-system, which is designed to handle that event, responds to it.

(2) **Interrupt-driven models:** These are exclusively used in real-time systems where an interrupt handler detects external interrupts. They are then passed to some other component for processing.

Broadcast models are effective in integrating sub-systems distributed across different computers on a network. Interrupt-driven models are used in real-time systems with stringent timing requirements.

The advantage of this approach to control is that it allows very fast responses to events to be implemented. Its disadvantages are that it is complex to program and difficult to validate.

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