Converting Decimal To Binary

Introduction

Converting decimal numbers to binary is a fundamental operation in computer science and digital systems. The binary number system, consisting of 0s and 1s, is widely used in computing and represents the foundation of digital data representation.

Approach

To convert a decimal number to binary, we can follow the following approach:

1. Start with the given decimal number.

2. Divide the decimal number by 2.

3. Record the remainder (0 or 1).

4. Repeat steps 2 and 3 with the quotient obtained from the previous division until the quotient becomes zero.

5. Concatenate the remainders obtained in reverse order to obtain the binary representation.

Step-by-Step Solution

Let's illustrate the conversion process using an example:

Example

Convert the decimal number 42 to binary.

Step 1: Start with the decimal number 42. 

Step 2: Divide 42 by 2. The quotient is 21, and the remainder is 0. 

Step 3: Divide 21 by 2. The quotient is 10, and the remainder is 1. 

Step 4: Divide 10 by 2. The quotient is 5, and the remainder is 0. 

Step 5: Divide 5 by 2. The quotient is 2, and the remainder is 1. 

Step 6: Divide 2 by 2. The quotient is 1, and the remainder is 0. 

Step 7: Divide 1 by 2. The quotient is 0, and the remainder is 1.

Recording the remainders in reverse order, we obtain the binary representation: 101010.

Code

Here's an example implementation for converting a decimal number to binary: