Interactive Binary Visualizer

Welcome to the binary learning tool! This tool helps you intuitively understand the relationship between binary and decimal numbers.

How to Use:

Method 1: Click the buttons. Click the circular buttons below to toggle them between **0** and **1**. Observe how the decimal value above changes with each click.
Method 2: Enter a decimal number. Type a decimal number between 0 and 255 into the input box below and press Enter. The binary bits will automatically update to show the corresponding combination.

Below each button is a number representing its 'place value,' which is its decimal value in the calculation. For example, the rightmost bit's place value is $2^0 = 1$, the second is $2^1 = 2$, and so on. Adding up the place values of all the buttons that are '1' gives you the total decimal number.

Binary Quiz

Using the learning tool above, see if you can answer the following question:

If a byte (8 bits) is represented by the binary number 00101101, what is its decimal value?

A. 45

B. 77

C. 210

D. 101

Answer and Analysis

Correct Answer: A. 45

Analysis:

To convert the binary number 00101101 to decimal, we need to add up the place values of each position where there is a '1'. The place values are calculated from right to left, starting with $2^0$.

In this binary number, there are four positions with a value of 1:

The first '1' is on the far right, its place value is $2^0 = 1$.
The second '1' is at the 3rd position from the right, its place value is $2^2 = 4$.
The third '1' is at the 4th position from the right, its place value is $2^3 = 8$.
The fourth '1' is at the 6th position from the right, its place value is $2^5 = 32$.

Add up these place values:

$32 + 8 + 4 + 1 = 45$

Therefore, the decimal value for 00101101 is **45**.