To convert the binary number \( 1011_2 \) to base 5, we can first convert it to decimal (base 10) and then from decimal to base 5.
Step 1: Convert from binary (base 2) to decimal (base 10).
The binary number \( 1011_2 \) can be converted to decimal as follows:
- \( 1 \times 2^3 = 1 \times 8 = 8 \)
- \( 0 \times 2^2 = 0 \times 4 = 0 \)
- \( 1 \times 2^1 = 1 \times 2 = 2 \)
- \( 1 \times 2^0 = 1 \times 1 = 1 \)
Now, add these values together:
\[ 8 + 0 + 2 + 1 = 11 \]
So, \( 1011_2 = 11_{10} \).
Step 2: Convert from decimal (base 10) to base 5.
Now, we need to convert \( 11_{10} \) to base 5. We can do this by dividing by 5 and keeping track of the remainders:
- \( 11 \div 5 = 2 \) with a remainder of \( 1 \).
- \( 2 \div 5 = 0 \) with a remainder of \( 2 \).
Now we write the remainders in reverse order:
The remainders collected (from last to first) give us \( 21_5 \).
Final Result: The binary number \( 1011_2 \) is equal to \( 21_5 \).
1 answer