Decimal to any base

Successively divide and keep track of the remainder, and then reverse the place value

• i.e., $31_{10} → 31_{2}$
  • 31/2 = 15, remainder 1
  • 15/2 = 7, remainder 1
  • 7/2 = 3, remainder 1
  • 3/2 = 1, remainder 1
  • ½ = 0, remainder 1
• i.e., $31_{10} → 1F_{16}$
  • 31/16 = 1, remainder 15 (15th place in base 16 is f)
  • 1/16 = 0, remainder 1 (1st place in base 16 is 1)

Any base to decimal

How To Convert Hexadecimal to Decimal

Write out the powers of the base from least to most significant bit, and sum the products of the bits and powers

• i.e., $AB09_{16} → 43785_{10}$

  Hex number:	A	B	0	9
  Place in base	10	11	0	9
  Power of base	$16^3$	$16^2$	$16^1$	$16^0$
  Product, then sum $\downarrow$	40960	2816	0	9
  = 43785