Question

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

Answer 1

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:

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