Question

1010 base 2 to 5

Answer 1

To convert the binary number \( 1010_2 \) to base 5, we can follow these steps:

1. **Convert binary to decimal**.
2. **Convert decimal to base 5**.

### Step 1: Convert \( 1010_2 \) to decimal

To convert from binary to decimal, we can use the positional value of each digit. The binary number \( 1010_2 \) can be broken down as follows:

\[
1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0
\]

Calculating each term:

\[
= 1 \times 8 + 0 \times 4 + 1 \times 2 + 0 \times 1
\]
\[
= 8 + 0 + 2 + 0
\]
\[
= 10
\]

So, \( 1010_2 = 10_{10} \).

### Step 2: Convert decimal \( 10_{10} \) to base 5

Now, we will convert the decimal number \( 10 \) to base 5.

To do this, we divide the number by 5 and note the remainders:

1. \( 10 \div 5 = 2 \) with a remainder of \( 0 \).
2. \( 2 \div 5 = 0 \) with a remainder of \( 2 \).

Now we read the remainders from bottom to top. The remainders are \( 2 \) and \( 0 \), giving us:

\[
10_{10} = 20_5
\]

Putting it all together, the binary number \( 1010_2 \) converts to \( 20_5 \) in base 5.