Q1: Conversion of binary number 1010101000010111 to hexadecimal number is

ANS:C - AA17₁₆

First of all we divide given binary number into four digit pairs from right hand side. i.e-1010 1010 0001 0111.

Now we convert these pairs hexadecimal like.

1010 = 1*2^3+0*2^2+1*2^1+0*2^0=8+0+2+0 = 10 = A.

1010 = 1*2^3+0*2^2+1*2^2+0*2^0=8+0+2+0 = 10 = A.

0001 = 0*2^3+0*2^2+0*2^1+1*2^0=0+0+0+1 = 1.

0111 = 0*2^3+1*2^2+1*2^1+1*2^0=0+4+2+1 = 7.

So (1010101000010111)base 2=(AA17)base 16.

Because in hexadecimal 10=A, 11=B, 12=C, 13=D, 14=E, 15=F.