Question:easy

What is the decimal equivalent of binary number \(101101\)?

Show Hint

For binary-to-decimal conversion, remember: \[ 2^0=1,\quad2^1=2,\quad2^2=4,\quad2^3=8,\quad2^4=16,\quad2^5=32. \] These powers appear frequently in competitive examinations.
Updated On: Jun 8, 2026
  • \(43\)
  • \(45\)
  • \(47\)
  • \(49\)
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Understand binary place values.
In a binary number, each digit stands for a power of $2$. Counting from the right, the places are $2^0, 2^1, 2^2$ and so on.

Step 2: Write the number with its places.
The number is $101101$. From left to right the powers are:
\[ 2^5\ 2^4\ 2^3\ 2^2\ 2^1\ 2^0 \]
matching digits $1\ 0\ 1\ 1\ 0\ 1$.

Step 3: Keep only the places with a 1.
A $0$ contributes nothing, so we only add the places that hold a $1$: positions $2^5$, $2^3$, $2^2$, and $2^0$.

Step 4: Write those powers as numbers.
\[ 2^5 = 32,\quad 2^3 = 8,\quad 2^2 = 4,\quad 2^0 = 1 \]
Step 5: Add them up.
\[ 32 + 8 + 4 + 1 = 45 \]
Step 6: State the result.
So $101101$ in binary equals $45$ in decimal, which is option (B).
\[ \boxed{45} \]
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