-1630 in binary (2's complement on 16 bits) is: 1111 1001 1010 0010

$$(-1630)_{10}=(1111~1001~1010~0010)_2$$

To convert the number -1630 from decimal to binary, we first convert the positive number 1630 to binary, then encode the negative sign (2's complement).

1. absolute value conversion (1630)

Let's divide $1630$ by $2$ and note the remainder at each step:

• $1630 \div 2 = 815$, remainder 0
• $815 \div 2 = 407$, remainder 1
• $407 \div 2 = 203$, remainder 1
• $203 \div 2 = 101$, remainder 1
• $101 \div 2 = 50$, remainder 1
• $50 \div 2 = 25$, remainder 0
• $25 \div 2 = 12$, remainder 1
• $12 \div 2 = 6$, remainder 0
• $6 \div 2 = 3$, remainder 0
• $3 \div 2 = 1$, remainder 1
• $1 \div 2 = 0$, remainder 1

Reading the remainders from bottom to top, the binary conversion of $1630$ is :

$$(-1630)_ {10} = (11001011110)_2$$

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 14401630 (11001011110)

• Inverted: 00110100001

Step 2 : Add 1

• 00110100001 + 1 = 00110100010

Step 3 : Complete with 1s

• Add 1's to obtain a 16-bit representation: 1111 1001 1010 0010

On 16 bits, this gives :

$$(-1630)_{10}=(1111~1001~1010~0010)_2$$