Question

Convert to binary

a) Convert 289₁₀ to binary using subtraction or division remainder. Show your work.

b) Convert BF₁₆ to binary. Show your work

Answer 1

a)
Divide 289 successively by 2 until the quotient is 0
   > 289/2 = 144, remainder is 1
   > 144/2 = 72, remainder is 0
   > 72/2 = 36, remainder is 0
   > 36/2 = 18, remainder is 0
   > 18/2 = 9, remainder is 0
   > 9/2 = 4, remainder is 1
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 100100001
So, 289 of decimal is 100100001 in binary
Answer: 100100001

b)
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 hexadecimal to binary
Converting BF to binary
B => 1011
F => 1111
So, in binary BF is 10111111
Answer: 10111111