Question

(a) Hexadecimal numbers are numbers in base 16. They use the following sixteen

digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are widely used in com-
puting, for example, to represent colors or network addresses of computers.

i. Convert A2F1316 to decimal. Show your work.
ii. Convert 456710 into hexadecimal. Show your work.
iii. Convert 00010101100011002 to hexadecimal. Explain how can you use
the fact that 16 = 24
?

iv. If you convert a 64-bit binary number into hexadecimal, how many hexadecimal digits does it have? Explain.

Answer 1

i)
=> A2F13
=> Ax16^4+2x16^3+Fx16^2+1x16^1+3x16^0
=> Ax65536+2x4096+Fx256+1x16+3x1
=> 10x65536+2x4096+15x256+1x16+3x1
=> 667411
Answer: 667411

ii)
Divide 4567 successively by 16 until the quotient is 0
4567/16 = 285, remainder is 7
285/16 = 17, remainder is 13
17/16 = 1, remainder is 1
1/16 = 0, remainder is 1
Read remainders from the bottom to top as 11D7
Answer: 0x11D7

iii)
Hexadecimal     Binary
    0           0000
    1           0001
    2           0010
    3           0011
    4           0100
    5           0101
    6           0110
    7           0111
    8           1000
    9           1001
    A           1010
    B           1011
    C           1100
    D           1101
    E           1110
    F           1111
Use this table to convert from binary to hexadecimal
Converting 0001010110001100 to hexadecimal
0001 => 1
0101 => 5
1000 => 8
1100 => C
So, in hexadecimal 0001010110001100 is 0x158C
Answer: 0x158C

iv)
each 4-bit binary is converted to a single symbol of hexadecimal
so, 64-bits binary is converted to 64/4 = 16 digits of hexadecimal
Answer: 16