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)

0101 0001 = 81Jul 24 16:23 UTC (GMT)
1001 1111 = -31Jul 24 16:08 UTC (GMT)
1010 1001 = -41Jul 24 16:01 UTC (GMT)
0111 0011 = 115Jul 24 15:55 UTC (GMT)
1001 0100 = -20Jul 24 15:50 UTC (GMT)
0111 1111 1111 1111 = 32,767Jul 24 15:50 UTC (GMT)
1001 1011 = -27Jul 24 15:46 UTC (GMT)
0001 1101 = 29Jul 24 15:44 UTC (GMT)
0111 = 7Jul 24 15:43 UTC (GMT)
1001 1111 = -31Jul 24 15:43 UTC (GMT)
0011 1100 = 60Jul 24 15:42 UTC (GMT)
0011 0011 = 51Jul 24 15:42 UTC (GMT)
1100 0000 = -64Jul 24 15:42 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