Decimal Equivalent of Binary Number (11001.011)

To find the decimal equivalent of a binary number, we need to understand the value of each digit in the binary number system. The binary number system is a base-2 system, meaning it uses only two digits: 0 and 1. Each digit in a binary number represents a power of 2.

Step 1: Understanding the Binary Number
The given binary number is (11001.011). Let's break it down into two parts: the integer part and the fractional part.

Integer Part: 11001
Fractional Part: 011

Step 2: Converting the Integer Part to Decimal
To convert the integer part from binary to decimal, we can use the place value method. Starting from the rightmost digit, we assign powers of 2 to each digit, increasing from right to left.

11001 = (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 16 + 8 + 0 + 0 + 1
= 25

So, the integer part (11001) in binary is equal to 25 in decimal.

Step 3: Converting the Fractional Part to Decimal
To convert the fractional part from binary to decimal, we use negative powers of 2. Starting from the leftmost digit after the decimal point, we assign negative powers of 2 to each digit, decreasing from left to right.

0.011 = (0 * 2^-1) + (1 * 2^-2) + (1 * 2^-3)
= 0 + 0.25 + 0.125
= 0.375

So, the fractional part (0.011) in binary is equal to 0.375 in decimal.

Step 4: Combining the Integer and Fractional Parts
To find the decimal equivalent of the given binary number (11001.011), we combine the values obtained from the integer and fractional parts.

Decimal Equivalent = Integer Part + Fractional Part
= 25 + 0.375
= 25.375

Therefore, the decimal equivalent of the binary number (11001.011) is 25.375.