Bytesize CS

Binary to denary

Work out the denary (base 10) value of each binary number. Turn off the place values when you're ready for a challenge.

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How to convert binary to denary
  1. Write the place values above the bits. From the right they double each time: 1, 2, 4, 8, 16, 32, 64, 128.
  2. Find every column that has a 1 in it.
  3. Add up the place values of those columns. Columns with a 0 add nothing.

Example: 0100 0101 has 1s under 64, 4 and 1, so it is 64 + 4 + 1 = 69.

Two's complement (A level): the leftmost bit is worth −128 instead of 128. Add the place values in the same way. If the leftmost bit is 1, the answer is negative. Example: 1000 0101 is −128 + 4 + 1 = −123.