-297 in binary (2's complement on 16 bits) is: 1111 1110 1101 0111

$$(-297)_{10}=(1111~1110~1101~0111)_2$$

To convert the number -297 from decimal to binary, we first convert the positive number 297 to binary, then encode the negative sign (2's complement).

1. absolute value conversion (297)

Let's divide $297$ by $2$ and note the remainder at each step:

• $297 \div 2 = 148$, remainder 1
• $148 \div 2 = 74$, remainder 0
• $74 \div 2 = 37$, remainder 0
• $37 \div 2 = 18$, remainder 1
• $18 \div 2 = 9$, remainder 0
• $9 \div 2 = 4$, remainder 1
• $4 \div 2 = 2$, remainder 0
• $2 \div 2 = 1$, remainder 0
• $1 \div 2 = 0$, remainder 1

Reading the remainders from bottom to top, the binary conversion of $297$ is :

$$(-297)_ {10} = (100101001)_2$$

2. Negative sign

The negative sign is represented by the 2's complement. Invert each bit and add 1 to the result:

Step 1: invert the bits of 1440297 (100101001)

• Inverted: 011010110

Step 2 : Add 1

• 011010110 + 1 = 011010111

Step 3 : Complete with 1s

• Add 1's to obtain a 16-bit representation: 1111 1110 1101 0111

On 16 bits, this gives :

$$(-297)_{10}=(1111~1110~1101~0111)_2$$