-62 in binary (2's complement on 16 bits) is: 1100 0010

$$(-62)_{10}=(1100~0010)_2$$

To convert the number -62 from decimal to binary, we first convert the positive number 62 to binary, then encode the negative sign (2's complement).

1. absolute value conversion (62)

Let's divide $62$ by $2$ and note the remainder at each step:

• $62 \div 2 = 31$, remainder 0
• $31 \div 2 = 15$, remainder 1
• $15 \div 2 = 7$, remainder 1
• $7 \div 2 = 3$, 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 $62$ is :

$$(-62)_ {10} = (111110)_2$$

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 144062 (111110)

• Inverted: 000001

Step 2 : Add 1

• 000001 + 1 = 000010

Step 3 : Complete with 1s

• Add 1's to obtain a 8-bit representation: 1100 0010

On 8 bits, this gives :

$$(-62)_{10}=(1100~0010)_2$$