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Left-Right Decimal to Binary
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[Binary To Decimal Conversions] [Left-Right Decimal to Binary] [Right-Left Decimal to Binary] [Binary To Hex Conversions] [Hex To Decimal Conversions] [Right-Left Hex to Binary]
Here are several examples conversions from decimal to binary using the left-to-right method. To convert the decimal number n, do this:
  1. Choose the largest power of two less than or equal to n. Call it p.
  2. Generate the initial one of your result.
  3. Subtract p from n.
  4. Divide p by 2.
  5. Repeat as indicated:
    1. if n is less than p, append a 0 to your solution.
    2. if n is greater or eqaul to p, append a 1 to your solution and subtract p from n.
    3. If p is 1, stop. Otherwise, divide p by two and return to step a.
Just like this:
  • 89210 = 11011111002:
    29 = 512 892 − 512 = 380 ⇒ 1
    28 = 256 380 − 256 = 124 ⇒ 1
    27 = 128 ⇒ 0
    26 = 64 124 − 64 = 60 ⇒ 1
    25 = 32 60 − 32 = 28 ⇒ 1
    24 = 16 28 − 16 = 12 ⇒ 1
    23 = 8 12 − 8 = 4 ⇒ 1
    22 = 4 4 − 4 = 0 ⇒ 1
    21 = 2 ⇒ 0
    20 = 1 ⇒ 0
  • 7110 = 10001112:
    26 = 64 71 − 64 = 7 ⇒ 1
    25 = 32 ⇒ 0
    24 = 16 ⇒ 0
    23 = 8 ⇒ 0
    22 = 4 7 − 4 = 3 ⇒ 1
    21 = 2 3 − 2 = 1 ⇒ 1
    20 = 1 1 − 1 = 0 ⇒ 1
  • 3310 = 1000012:
    25 = 32 33 − 32 = 1 ⇒ 1
    24 = 16 ⇒ 0
    23 = 8 ⇒ 0
    22 = 4 ⇒ 0
    21 = 2 ⇒ 0
    20 = 1 1 − 1 = 0 ⇒ 1
  • 19610 = 110001002:
    27 = 128 196 − 128 = 68 ⇒ 1
    26 = 64 68 − 64 = 4 ⇒ 1
    25 = 32 ⇒ 0
    24 = 16 ⇒ 0
    23 = 8 ⇒ 0
    22 = 4 4 − 4 = 0 ⇒ 1
    21 = 2 ⇒ 0
    20 = 1 ⇒ 0