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)

1000 0110 = -6Jan 18 09:55 UTC (GMT)
1001 1110 = -30Jan 18 09:39 UTC (GMT)
11 = -1Jan 18 09:39 UTC (GMT)
0110 = 6Jan 18 09:39 UTC (GMT)
0111 = 7Jan 18 09:39 UTC (GMT)
1111 0000 = -112Jan 18 09:39 UTC (GMT)
0110 0101 1001 0011 0100 0000 0000 0000 = 1,704,148,992Jan 18 09:39 UTC (GMT)
0011 0101 = 53Jan 18 09:38 UTC (GMT)
1000 0001 0111 0100 = -372Jan 18 09:38 UTC (GMT)
0011 1001 = 57Jan 18 09:38 UTC (GMT)
1011 1011 = -59Jan 18 09:38 UTC (GMT)
0100 1010 = 74Jan 18 09:38 UTC (GMT)
1000 1010 = -10Jan 18 09:38 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