Question

if hexadecimal number FA16 represent a signed number in two compliments, what the decimal representation of that number? include the sign for that number with no spaces between the number and sign.

Answer 1

The given hexadecimal number is:

= FA16

The base of the hexadecimal number system is 16 and this number system uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.

In binary representation, a hexadecimal digit is represented by using a group of four-digit from right to left.

The equivalent binary number is:

= 1111101000010110

The MSB of the above binary number is 1, so this is a negative number.

We needs to do the two's complement of the above number to get the actual number.

The two's complement of the above number is:

0000010111101010

The decimal equivalent of the above binary number is:

= 1x2¹⁰ + 0x2⁹ + 1x2⁸ + 1x2⁷ + 1x2⁶ + 1x2⁵ + 0x2⁴ + 1x2³ + 0x2² + 1x2¹ + 0x2⁰

= 1514

The actual number is = -1514