-658 in binary (2's complement on 16 bits) is: 1111 1101 0110 1110

$$(-658)_{10}=(1111~1101~0110~1110)_2$$

To convert the number -658 from decimal to binary, we first convert the positive number 658 to binary, then encode the negative sign (2's complement).

1. absolute value conversion (658)

Let's divide $658$ by $2$ and note the remainder at each step:

• $658 \div 2 = 329$, remainder 0
• $329 \div 2 = 164$, remainder 1
• $164 \div 2 = 82$, remainder 0
• $82 \div 2 = 41$, remainder 0
• $41 \div 2 = 20$, remainder 1
• $20 \div 2 = 10$, 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

Reading the remainders from bottom to top, the binary conversion of $658$ is :

$$(-658)_ {10} = (1010010010)_2$$

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 1440658 (1010010010)

• Inverted: 0101101101

Step 2 : Add 1

• 0101101101 + 1 = 0101101110

Step 3 : Complete with 1s

• Add 1's to obtain a 16-bit representation: 1111 1101 0110 1110

On 16 bits, this gives :

$$(-658)_{10}=(1111~1101~0110~1110)_2$$