Stacks and their applications in C++

Binary To Decimal Conversion

(Converting a Number from Binary to Decimal) The language of a computer, called machine language, is a sequence of 0s and 1s. When you press the key A on the keyboard, 01000001 is stored in the computer. Also, the collating sequence of A in the ASCII character set is 65. In fact, the binary representation of A is 01000001 and the decimal representation of A is 65.

The numbering system we use is called the decimal system, or base 10 system. The numbering system that the computer uses is called the binary system, or base 2 system. The purpose of this exercise is to write a function to convert a number from base 2 to base 10.

To convert a number from base 2 to base 10, we first find the weight of each bit in the binary number. The weight of each bit in the binary number is assigned from right to left. The weight of the rightmost bit is 0. The weight of the bit immediately to the left of the rightmost bit is 1, the weight of the bit immediately to the left of it is 2, and so on. Consider the binary number

1001101. The weight of each bit is as follows:

Weight 6 5 4 3 2 1 0

1 0 0 1 1 0 1

We use the weight of each bit to find the equivalent decimal number. For each bit, we multiply the bit by 2 to the power of its weight, and then we add all of the numbers. For the binary number 1001101, the equivalent decimal number is

To write a program that converts a binary number into the equivalent decimal number, we note two things: (1) The weight of each bit in the binary number must be known, and (2) the weight is assigned from right to left. Because we do not know in advance how many bits are in the binary

number, we must process the bits from right to left. After processing a bit, we can add 1 to its weight, giving the weight of the bit immediately to its left. Also, each bit must be extracted from the binary number and multiplied by 2 to the power of its weight. To extract a bit, you can use the mod operator.

int convertBinaryToInt(char binString[])

{

Stack s;

int res;

//your implementation

return res;

Postfix Calculator:

Write a program that will read postfix expression that may contain only integer numbers and operators (consider only binary operators: /, *, -, and + ) which are delimited by single or more white space. Then the program will calculate the value of the expression and print it.

(If input postfix expression is not valid appropriate error message will be printed such as missing operand, missing operator or invalid symbol in the expression)

Infix to Postfix

Write a program that converts an infix expression into an equivalent postfix expression. The rules to convert an infix expression into an equivalent postfix expression are as follows:

Suppose infx represents the infix expression and pfx represents the postfix expression.

The rules to convert infx into pfx are as follows:

1) Initialize pfx to an empty expression and also initialize the stack.

2) While there are symbols in the infx expression, Get the next symbol, sym, from infx.

a) If sym is an operand, append sym to pfx.

b) If sym is (, push sym into the stack.

c) If sym is ), pop and append all the symbols from the stack until the most recent left parenthesis. Pop and discard the left parenthesis.

d) If sym is an operator:

i) If s is not empty ,Pop and append all the operators from the stack to pfx that are above the most recent left parenthesis and have precedence greater than or equal to sym.

ii) Push sym onto the stack.

3) After processing infx, some operators might be left in the stack. Pop and append to pfx everything from the stack.

In this program, you will consider the (binary) arithmetic operators: +, -, *, and /, operands are single letters. In valid infix expression operands and operators are delimited with one or more white space.

You may assume that the expressions you will process are error free.

Design a class that stores the infix and postfix strings. The class must include the following operations:

-infix: string

-postfix: string

+getInfixStores the infix expression

+showInfixOutputs the infix expression

+showPostfixOutputs the postfix expression

Some other operations that you might need are the following:

+convertToPostfixConverts the infix expression into a postfix expression. The resulting postfix expression is stored in pfx.

-precedenceDetermines the precedence between two operators. If the first operator is higher or equal precedence than the second operator, it returns the value true; otherwise, it returns the value false.

Include the constructors and destructors for automatic initialization and dynamic memory deallocation.

Test your program on the following five expressions:

A + B - C;

(A + B ) * C;

(A + B) * (C - D);

A + ((B + C) * (E - F) - G) / (H - I);

A + B * (C + D ) - E / F * G + H;

For each expression, your answer must be in the following form:

Infix Expression: A + B - C;

Postfix Expression: A B + C -