how is 657 base ten expressed in hexadecimals?

Hi!!


First we must define the Hexadecimal symbols in Decimals:

 Hex. Dec.
  0 -> 0 
  1 -> 1 
  2 -> 3 
  3 -> 3 
  4 -> 4 
  5 -> 5 
  6 -> 6 
  7 -> 7 
  8 -> 8 
  9 -> 9 
  A -> 10 
  B -> 11
  C -> 12
  D -> 13
  E -> 14
  F -> 15

Steps to convert decimal numbers to hexadecimal: 
1· Divide the decimal by 16. 
2· Write down the remainder (in hex). 
3· Divide the result by 16. 
4· Repeat step 2 and 3 until result is 0. 
5. The hex value is the digit sequence of the remainders from the last to first. 

For this problem is:
657/16 --> Result = 41; Remainder = 1 -> 1
41/16 --> Result = 2; Remainder = 9 -> 9
2/16 --> Result = 0; Remainder = 2 -> 2

The hex value of the decimal number 657 is 291.


What we did?

By the sucesive divisions we found that:
657 = 41*16^1 + 1*16^0
41 = 2*16^1 + 9*16^0
2 = 0*16^1 + 2*16^0

Then:
657 = 41*16^1 + 1*16^0 = 
    = (2*16^1 + 9*16^0)*16^1 + 1*16^0 =
    = [(0*16^1 + 2*16^0)*16^1 + 9*16^0]*16^1 + 1*16^0 =
    = [2*16^1 + 9*16^0]*16^1 + 1*16^0 =
    = 2*16^2 + 9*16^1 + 1*16^0 =
    = 291 in HEXadecimal
   

657 in dec = 291 in hex means that 657 is equal to 2*16^2 + 9*16^1 +
1*16^0; in effect is:

2*16^2 = 512
9*16^1 = 144
1*16^0 =   1
------  -----
 291 --> 657
(Hex)   (Decimal)


Hope that this helps you. Feel free to request for a clarification if you need it.

Regards.
livioflores-ga

Thanks for really helping me to understand how you arrived at your answer!

Unless this is a trick question, the answer is 291 . . .

That was fantastic!!!