What is the decimal conversion of binary 1111111111111111?

Answer 1

1111111111111111 to base 2 (binary) is equivalent to

FFFF to the base 16 (hexadecimal) which in decimal equals

(15 x 16*3) + (15 x 16*2) + (15 x 16*1) + (15 x 16*0) =

(15 x 4096) + (15 x 256) + (15 x 16) + (15 x 1) =

61440 + 3840 + 240 + 15 = 65535

Another way to look at this is that FFFF in hexadecimal is actually 10000 in hexadecimal minus 1 and we know 10000 in hexadecimal is 65536 and so FFFF in hexadecimal is 65536-1 = 65535