Question

Write an application that inputs an integer containing only 0 s and 1 s (i.e., a binary integer) and prints its decimal equivalent. [Hint: Use the remainder and division operators to pick off the binary number's digits one at a time, from right to left. In the decimal number system, the rightmost digit has a positional value of 1 and the next digit to the left has a positional value of \(10,\) then 100 , then \(1000,\) and so on. The decimal number 234 can be interpreted as \(4^{*} 1+3^{*} 10+2^{*} 100 .\) In the binary number system, the rightmost digit has a positional value of 1 , the next digit to the left has a positional value of \(2,\) then \(4,\) then \(8,\) and so on. The decimal equivalent of binary 1101 is \(1^{*}\) \(1+0^{*} 2+1^{*} 4+1^{*} 8,\) or \(1+0+4+8\) or, 13.1

Short answer

Convert each binary digit to decimal value, sum them, and output the result.

Step-by-step solution

Identify the Binary Number

Understand that the input is a binary number containing only 0s and 1s, such as '1101'. Recognize that the binary system is base 2.

Initialize Variables

Prepare variables to keep track of the current power of 2 (starting from 0) and the decimal result (starting from 0). For example, let `power = 0` and `decimal = 0`.

Loop Through Binary Digits

Use a loop to go through each digit of the binary number from right to left. In each iteration, extract the rightmost digit using the modulo operator (`digit = binary_number % 10`).

Calculate the Contribution of Each Digit

For each binary digit obtained, multiply it by 2 raised to the current power. Add this product to the decimal equivalent. Update the power of 2 by 1 for the next digit. For example: if digit is 1 and power is 3, add `1 * 2^3 = 8` to the decimal value.

Update Binary Number

Divide the binary number by 10 to remove the rightmost digit (use integer division). For example, if the binary number is 1101, dividing by 10 gives 110.

Repeat Steps 3-5

Continue looping through steps 3, 4, and 5 until there are no more digits left in the binary number.

Output the Decimal Equivalent

Once the loop completes, the decimal variable contains the final decimal equivalent of the given binary number. Print or return this value.

Key concepts

Integer Operations

Integer operations are basic arithmetic calculations involving whole numbers. These operations include addition, subtraction, multiplication, and division. In computer programming, understanding integer operations is crucial as they form the basis for most algorithms and computations.
In this exercise, integer operations help in converting a binary number to its decimal equivalent. For example, multiplying each binary digit by powers of 2 involves integer multiplication. Similarly, integer division helps in removing digits from the binary number step by step. This precise use of integer operations ensures accurate conversion.

Base Number Systems

Base number systems define how numbers are represented using different bases. The binary system is base 2, using only the digits 0 and 1. Meanwhile, the decimal system is base 10, which uses digits from 0 to 9. Understanding various base systems is essential, especially in computer science, where binary is dominant.
This exercise highlights the conversion from the binary base to the decimal base. In the binary system, each digit represents an increasing power of 2, while in the decimal system, each digit represents an increasing power of 10. Recognizing these positional values is key to correctly converting between these systems.

Loop Structures

Loop structures in programming allow for the repetitive execution of a block of code. They are fundamental for tasks that require iteration, such as processing each digit of a number. In this exercise, a loop is used to traverse the binary digits from right to left.
The loop continues until all digits have been processed. For each iteration, operations are performed to extract the digit and calculate its contribution to the decimal result. Using loops helps efficiently manage and automate the repetitive tasks required during conversion.

Modulo Operator

The modulo operator is used to find the remainder of a division operation. It is represented by the symbol `%`. This operator is particularly useful in programming exercises where digit extraction is necessary.
In the current exercise, the modulo operator assists in extracting the rightmost digit of a binary number. By applying `binary_number % 10`, it isolates the last digit of the number. This is essential for accurately assessing the value of each binary digit during conversion to decimal.

Educational Programming Exercise

Educational programming exercises are designed to enhance understanding and practice of specific concepts. They offer students the opportunity to apply theoretical knowledge practically. This particular exercise focuses on converting a binary number to a decimal number.
It integrates various core concepts like integer operations, base number systems, loop structures, and the modulo operator. By combining these elements, the exercise facilitates a comprehensive learning experience, teaching students not only about binary numbers but also essential programming structures and logic.