Answer
The binary core for $Y$ is:
$1011001$
Work Step by Step
The essay states that the uppercase letter $Y$ is assigned the number $89$.
To find the binary representation for this, use division.
The place values in base two are $..., 2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, 1$
The place values that are less than or equal to $89$ are $2^6, 2^5, 2^4, 2^3, 2^2, 2^1$ and $1$.
Divide $89$ by $2^6$ or $64$:
$89 \div 64 = 1$ remainder $25$
Divide $25$ by $2^5$ or $32$
$25 \div 32 = 0$ remainder $25$
Divide $25$ by $2^4$ or $16$:
$25 \div 16 = 1$ remainder $9$
Divide $9$ by $2^3$ or $8$:
$9 \div 8 = 1$ remainder $1$
Divide $1$ by $2^2$:
$1 \div 4=0$ remainder $1$
Divide $1$ by $2^1$ or $2$:
$1 \div 2 = 0$ remainder $1$
Divide $1$ by $1$:
$1 \div 1 = 1$
Thus,
$89 = (1 \times 2^6) + (0 \times 2^5) + (1 \times 2^4)+(1 \times 2^3)+(0\times 2^2) + (0 \times 2)+(1 \times 1)
\\89=1011001_{\text{two}}$
