5.625 2 - JavaScript

JavaScript is a programming language that is commonly used for creating dynamic and interactive web pages. One of its features is its ability to handle decimal numbers with precision. In this article, we will explore how JavaScript handles decimal numbers and specifically focus on the decimal number 5.625 2.

Working with Decimal Numbers in JavaScript

JavaScript has two types of numbers: integers and decimals. Integers are whole numbers while decimals represent numbers with a fractional component. To declare a decimal number in JavaScript, we can use the following syntax:

let decimalNumber = 5.625;

JavaScript can handle decimal numbers with precision because it uses the IEEE 754 standard to represent them internally. This standard uses a fixed number of bits to represent a decimal number, which means that the more bits are used, the more precise the number will be.

Decimal to Binary Conversion

To understand how JavaScript handles the decimal number 5.625 2, we need to convert it to binary. Binary is a number system that uses two digits (0 and 1) to represent numbers. To convert decimal to binary, we divide the decimal number by 2 repeatedly and write the remainder in reverse order. For example, to convert 5 to binary, we perform the following steps:

5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1

So, 5 in binary is 101 2.

To convert 0.625 to binary, we multiply it by 2 repeatedly until we get a whole number. We write down the integer part and continue with the fractional part. For example:

0.625 × 2 = 1.25 → 1
0.25 × 2 = 0.5 → 0
0.5 × 2 = 1 → 1

So, 0.625 in binary is 0.101 2.

Therefore, 5.625 in binary is:

101.101 2

Binary to Decimal Conversion

To convert binary to decimal, we multiply each binary digit by its corresponding power of 2 and add up the results. For example:

1 × 2^2 + 0 × 2^1 + 1 × 2^0 + 1 × 2^-1 + 0 × 2^-2 + 1 × 2^-3 = 5.625

So, 101.101 2 in decimal is 5.625.

Conclusion

JavaScript uses the IEEE 754 standard to handle decimal numbers with precision. The decimal number 5.625 2 in binary is 101.101 2 and in decimal is 5.625. Understanding how JavaScript handles decimal numbers is important for creating accurate and reliable programs.