-1440 in binary (2's complement on 16 bits) is: 1111 1010 0110 0000

$$(-1440)_{10}=(1111~1010~0110~0000)_2$$

To convert the number -1440 from decimal to binary, we first convert the positive number 1440 to binary, then encode the negative sign (2's complement).

1. Absolute Value Conversion (1440)

Let's divide $1440$ by $2$ and note the remainder at each step:

• $1440 \div 2 = 720$, remainder 0
• $720 \div 2 = 360$, remainder 0
• $360 \div 2 = 180$, remainder 0
• $180 \div 2 = 90$, remainder 0
• $90 \div 2 = 45$, remainder 0
• $45 \div 2 = 22$, remainder 1
• $22 \div 2 = 11$, remainder 0
• $11 \div 2 = 5$, remainder 1
• $5 \div 2 = 2$, 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 $1440$ is :

$$(-1440)_ {10} = (10110100000)_2$$

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 14401440 (10110100000)

• Inverted: 01001011111

Step 2 : Add 1

• 01001011111 + 1 = 01001100000

Step 3 : Complete with 1s

• Add 1's to obtain a 16-bit representation: 1111 1010 0110 0000

On 16 bits, this gives :

$$(-1440)_{10}=(1111~1010~0110~0000)_2$$