1110 base 2 to 5

Answer 1

To convert the binary number \( 1110_2 \) (base 2) to base 5, we can follow these steps:

1. Convert the binary number to decimal (base 10).
2. Convert the decimal number to base 5.

Step 1: Convert from binary to decimal.

The binary number \( 1110_2 \) can be converted to decimal by calculating:

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

Calculating each term gives us:

\[ 1 \times 8 + 1 \times 4 + 1 \times 2 + 0 \times 1 = 8 + 4 + 2 + 0 = 14 \]

So, \( 1110_2 = 14_{10} \).

Step 2: Convert from decimal to base 5.

Now we convert \( 14_{10} \) to base 5 by dividing by 5 and recording the remainders:

1. \( 14 \div 5 = 2 \) remainder \( 4 \)
2. \( 2 \div 5 = 0 \) remainder \( 2 \)

Now, we write the remainders in reverse order:

So, \( 14_{10} = 24_5 \).

Therefore, the binary number \( 1110_2 \) converts to \( 24_5 \) in base 5.