P is a 16-bit signed integer. The 2's complement representation of P is…

In binary arithmetic, multiplying a signed integer by 8 (which is 23) is exactly equivalent to shifting the bits to the left by 3 positions (<< 3).

1. Convert P from Hexadecimal to Binary:

   P = (F87B)16

   • F = 1111

   • 8 = 1000

   • 7 = 0111

   • B = 1011

   P = (1111 1000 0111 1011)2

2. Shift Left by 3 Bits (P X 23):

   When shifting a 16-bit number left by 3 bits, the 3 leftmost bits drop off, and 3 zeros are introduced on the right side:

   • Original: 1111 1000 0111 1011

   • Shifted: 1100 0011 1101 1000

3. Convert back to Hexadecimal:

   Group the resulting binary string into sets of 4 bits from left to right:

   • 1100 = C

   • 0011 = 3

   • 1101 = D

   • 1000 = 8

   Result = (C3D8)16