-647 in binary (two's complement in a 16-bit representation) is : 1111 1101 0111 1001
$$(-647)_{10} = (1111~1101~0111~1001)_{2}$$

To convert the decimal number $-647$ to binary, we follow these steps:

1. Convert the absolute value:

   • First, convert $647$ (ignoring the negative sign) to binary.

   • Divide by 2 and record the remainders:

     • $647 \div 2 = 323$ remainder $1$
     • $323 \div 2 = 161$ remainder $1$
     • $161 \div 2 = 80$ remainder $1$
     • $80 \div 2 = 40$ remainder $0$
     • $40 \div 2 = 20$ remainder $0$
     • $20 \div 2 = 10$ remainder $0$
     • $10 \div 2 = 5$ remainder $0$
     • $5 \div 2 = 2$ remainder $1$
     • $2 \div 2 = 1$ remainder $0$
     • $1 \div 2 = 0$ remainder $1$

     So, $647_{10} = 1010000111_2$.

2. Account for the negative sign:

   • Using two's complement representation for negative numbers, you invert the binary digits and add $1$.

   Step 1: Invert the bits of $647$ (1010000111):

   • Inverted: $0101111000$

   Step 2: Add 1:

   • $0101111000 + 1 = 0101111001$

   Step 3: Prepend 1:

   • Prepend 1 to get a 16-bit representation : $1111~1101~0111~1001$

Thus, $-647_{10}$ in binary (using two's complement in a 16-bit representation) is $1111~1101~0111~1001_2$.