Question

Convert the following decimal number to twos complement binary numbers using 16 digits:

a.) -35
b.) -1

Answer 1

Two's complement conversion of -35 and -1 to 16-digit binary numbers results in 1111111111011101 and 1111111111111111, respectively.

Step-by-step explanation:

To convert the decimal number -35 to two's complement binary using 16 digits, follow these steps:

1. Convert the absolute value of the number to binary: 35 in binary is 100011.
2. Pad the binary number to 16 bits: 0000000000100011.
3. Invert all the bits (0 to 1 and 1 to 0): 1111111111011100.
4. Add 1 to the inverted number: 1111111111011100 + 1 = 1111111111011101.

The two's complement binary representation of -35 using 16 digits is 1111111111011101.

To convert -1 to two's complement binary using 16 digits:

1. Convert the absolute value of the number to binary: 1 in binary is 1.
2. Pad the binary number to 16 bits: 0000000000000001.
3. Invert all bits: 1111111111111110.
4. Add 1 to the inverted number: 1111111111111110 + 1 = 1111111111111111.

The two's complement binary representation of -1 using 16 digits is 1111111111111111.