How to Convert 110.11 from Binary to Base 10

Welcome to understanding binary position values! Today we'll explore how binary numbers work using powers of two.Let's examine the binary number one one zero point one one.In binary, each position represents a power of two. Let's see how these positions are assigned.To the left of the decimal point, we start with two to the zero power and increase as we move left.To the right of the decimal point, we use negative powers of two, which decrease as we move further right.Here's a helpful reference table showing the actual values for each power of two we're using.The leftmost position is two to the second power, or four.Moving right, we have two to the first power, which is two.Then two to the zero power, which equals one.After the decimal point, we have two to the negative first power, or one half.And finally, two to the negative second power, which is one quarter.Now that we understand the position values, we're ready to calculate the actual value of this binary number.For the integer portion, we'll focus on the digits before the decimal point.We'll multiply each binary digit by its corresponding power of 2.Starting from the left, one times two to the power of two equals four.Next, one times two to the power of one equals two.Finally, zero times two to the power of zero equals zero.Now we add all these values: four plus two plus zero.This gives us six as the integer portion of our decimal conversion.Now we'll calculate the value of the fractional portion, the digits after the decimal point.These two digits correspond to negative powers of two: two to the negative one and two to the negative two.For the first digit, we multiply one times two to the negative one, which equals zero point five.For the second digit, we multiply one times two to the negative two, which equals zero point two five.Adding these decimal values: zero point five plus zero point two fiveGives us zero point seven five for the fractional portion.Finally, we combine this with our previously calculated integer portion of sixTo get our final answer in base ten: six point seven five.