-184 in binary (2's complement on 16 bits) is: 1111 1111 0100 1000

$$(-184)_{10}=(1111~1111~0100~1000)_2$$

To convert the number -184 from decimal to binary, we first convert the positive number 184 to binary, then encode the negative sign (2's complement).

1. absolute value conversion (184)

Let's divide $184$ by $2$ and note the remainder at each step:

• $184 \div 2 = 92$, remainder 0
• $92 \div 2 = 46$, remainder 0
• $46 \div 2 = 23$, remainder 0
• $23 \div 2 = 11$, remainder 1
• $11 \div 2 = 5$, 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 $184$ is :

$$(-184)_ {10} = (10111000)_2$$

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 1440184 (10111000)

• Inverted: 01000111

Step 2 : Add 1

• 01000111 + 1 = 01001000

Step 3 : Complete with 1s

• Add 1's to obtain a 16-bit representation: 1111 1111 0100 1000

On 16 bits, this gives :

$$(-184)_{10}=(1111~1111~0100~1000)_2$$