Converter from signed binary: converting to decimal system (base ten) integer numbers

Convert numbers from signed binary to integers in the decimal system (base ten)

First bit (leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.

Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - or else extra bits of '0' value will be added in front (to the left).

Latest signed binary numbers converted to signed integers in decimal system (base ten)

0001 1101 0001 0001 = 7,441Feb 21 18:42 UTC (GMT)
1011 1000 = -56Feb 21 18:41 UTC (GMT)
0110 1111 = 111Feb 21 18:37 UTC (GMT)
1110 = -6Feb 21 18:26 UTC (GMT)
0000 0000 0001 0110 1001 1111 1111 1101 = 1,482,749Feb 21 18:18 UTC (GMT)
1001 0101 1001 0111 = -5,527Feb 21 18:18 UTC (GMT)
1100 0010 = -66Feb 21 18:16 UTC (GMT)
1101 0010 = -82Feb 21 18:09 UTC (GMT)
1111 1010 = -122Feb 21 18:08 UTC (GMT)
1111 1010 = -122Feb 21 18:08 UTC (GMT)
1101 0010 = -82Feb 21 18:07 UTC (GMT)
1101 0010 = -82Feb 21 18:07 UTC (GMT)
1101 1001 = -89Feb 21 18:05 UTC (GMT)

How to convert signed binary numbers from binary system to decimal

To understand how to convert a signed binary number from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1110, to base ten:

  • In a signed binary, first bit (leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value (value without sign). The first bit is 1, so the number is negative.
  • Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding powers of 2 (numeral base), starting with zero, from the right of the number (rightmost bit), walking to the left of the number, increasing each corresonding power of 2 with exactly one unit, but ignoring the very first bit (the leftmost, the one representing the sign):
  • powers of 2   6 5 4 3 2 1 0
    number's digits 1 0 0 1 1 1 1 0
  • Build the representation of the positive number in base 10, by taking each digit of the binary number, multiplying it by the corresponding power of 2 and then summing up all the terms, but also taking care of the number sign:
    1001 1110 =
    = - (0 * 26 + 0 * 25 + 1 * 24 + 1 * 23 + 1 * 22 + 1 * 21 + 0 * 20) =
    = - (0 + 0 + 16 + 8 + 4 + 2 + 0) =
    = - (16 + 8 + 4 + 2) =
    = -30(10)
  • Binary signed number, 1001 1110 = -30(10), signed negative integer in base 10