-898 in binary (2's complement on 16 bits) is: 1111 1100 0111 1110

$$(-898)_{10}=(1111~1100~0111~1110)_2$$

To convert the number -898 from decimal to binary, we first convert the positive number 898 to binary, then encode the negative sign (2's complement).

1. absolute value conversion (898)

Let's divide $898$ by $2$ and note the remainder at each step:

• $898 \div 2 = 449$, remainder 0
• $449 \div 2 = 224$, remainder 1
• $224 \div 2 = 112$, remainder 0
• $112 \div 2 = 56$, remainder 0
• $56 \div 2 = 28$, remainder 0
• $28 \div 2 = 14$, remainder 0
• $14 \div 2 = 7$, remainder 0
• $7 \div 2 = 3$, remainder 1
• $3 \div 2 = 1$, remainder 1
• $1 \div 2 = 0$, remainder 1

Reading the remainders from bottom to top, the binary conversion of $898$ is :

$$(-898)_ {10} = (1110000010)_2$$

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 1440898 (1110000010)

• Inverted: 0001111101

Step 2 : Add 1

• 0001111101 + 1 = 0001111110

Step 3 : Complete with 1s

• Add 1's to obtain a 16-bit representation: 1111 1100 0111 1110

On 16 bits, this gives :

$$(-898)_{10}=(1111~1100~0111~1110)_2$$