$$(-1450)_{10}=(1111~1010~0101~0110)_2$$

To convert the number -1450 from decimal to binary, we first convert the positive number 1450 to binary, then encode the negative sign (2's complement).

1. absolute value conversion (1450)

Let's divide $1450$ by $2$ and note the remainder at each step:

• $1450 \div 2 = 725$, remainder 0
• $725 \div 2 = 362$, remainder 1
• $362 \div 2 = 181$, remainder 0
• $181 \div 2 = 90$, remainder 1
• $90 \div 2 = 45$, 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 $1450$ is :

$$(-1450)_ {10} = (10110101010)_2$$

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 1450 (10110101010)

• Inverted: 01001010101

Step 2 : Add 1

• 01001010101 + 1 = 01001010110

Step 3 : Complete with 1s

• Add 1's to obtain a 16-bit representation: 1111 1010 0101 0110

On 16 bits, this gives :

$$(-1450)_{10}=(1111~1010~0101~0110)_2$$