If 21y=1111 base two.Find the value of y ?

1 answer

To solve the equation \( 21y = 1111_2 \), we first need to convert \( 1111_2 \) (which is in binary) to decimal (base 10).

The binary number \( 1111_2 \) can be expanded as follows:

\[ 1111_2 = 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]

Calculating each term:

\[ = 1 \cdot 8 + 1 \cdot 4 + 1 \cdot 2 + 1 \cdot 1 \] \[ = 8 + 4 + 2 + 1 \] \[ = 15 \]

So, \( 1111_2 = 15_{10} \).

Now we have the equation:

\[ 21y = 15 \]

To find \( y \), we can divide both sides by 21:

\[ y = \frac{15}{21} \]

Simplifying \( \frac{15}{21} \):

\[ y = \frac{5}{7} \]

Thus, the value of \( y \) is:

\[ \boxed{\frac{5}{7}} \]