Related Bases 3

What about converting in the other direction?

Let's convert D5F8 hex to binary.

• start at the right end of the numeral
• convert each hex digit to a group of 4 bits; be sure to use all 4 bits, including leading zeroes
• 8 in binary is 1000
• F = 15, which is 1111
  • 15 divided by 2 is 7 with a remainder of 1
  • 7 divided by 2 is 3 with a remainder of 1
  • 3 divided by 2 is 1 with a remainder of 1
  • 1 divided by 2 is 0 with a remainder of 1
• 5 is 0101
• D = 13, which is 1101
  • 13 divided by 2 is 6 with a remainder of 1
  • 6 divided by 2 is 3 with a remainder of 0
  • 3 divided by 2 is 1 with a remainder of 1
  • 1 divided by 2 is 0 with a remainder of 1
  • that is 1101 (don't forget about the right-to-left part)
• now just stick them all together in the correct order:
• 1101-0101-1111-1000
• and removing the grouping markers we get 1101010111111000