Converter of signed binary numbers: converting to decimal system integers (base ten)

Convert signed binary numbers to integers in decimal system (base 10)

First bit (the 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 - otherwise extra bits on 0 will be added in front (to the left).

How to convert a signed binary number to an integer in base ten:

1) Construct the unsigned binary number: exclude the first bit (the leftmost); this bit is reserved for the sign, 1 = negative, 0 = positive and does not count when calculating the absolute value (without sign).

2) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

3) Add all the terms up to get the positive integer number in base ten.

4) Adjust the sign of the integer number by the first bit of the initial binary number.

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

0111 1100 0101 1010 = 31,834 Jun 13 23:52 UTC (GMT)
0011 0110 0011 1101 = 13,885 Jun 13 23:52 UTC (GMT)
1011 1011 0011 0111 0100 0010 1100 1000 = -993,477,320 Jun 13 23:52 UTC (GMT)
0111 1100 0101 0101 1111 1111 1101 1111 = 2,086,010,847 Jun 13 23:52 UTC (GMT)
1000 0011 0010 0000 = -800 Jun 13 23:52 UTC (GMT)
1010 0101 0000 0010 = -9,474 Jun 13 23:52 UTC (GMT)
1000 0000 0000 0000 0000 0000 0000 0110 = -6 Jun 13 23:52 UTC (GMT)
0000 1111 0001 1100 = 3,868 Jun 13 23:51 UTC (GMT)
1101 1110 0001 1111 = -24,095 Jun 13 23:51 UTC (GMT)
0001 0100 0001 0100 0001 0100 0001 0100 0001 0100 0001 0100 0001 0100 0001 1001 = 1,446,803,456,761,533,465 Jun 13 23:51 UTC (GMT)
0000 0000 1100 0010 0110 0100 1101 1000 0110 0000 1100 0010 0110 0100 1001 0001 = 54,717,025,980,933,265 Jun 13 23:51 UTC (GMT)
0000 0000 0000 0000 0000 0000 0000 1000 1011 0110 1001 0100 0100 1101 0010 1000 = 37,422,910,760 Jun 13 23:51 UTC (GMT)
1100 0011 0110 0010 = -17,250 Jun 13 23:50 UTC (GMT)
All the converted signed binary numbers to integers in base ten

How to convert signed binary numbers from binary system to decimal (base ten)

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 the binary number, 1001 1110, to base ten:

  • In a signed binary, the 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 our number is negative.
  • Write bellow the binary number in base two, and above each bit that makes up the binary number write the corresponding power of 2 (numeral base) that its place value represents, starting with zero, from the right of the number (rightmost bit), walking to the left of the number and increasing each corresonding power of 2 by 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
    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 adding all the terms up, but also taking care of the number sign:

    1001 1110 =


    - (0 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =


    - (0 + 0 + 16 + 8 + 4 + 2 + 0)(10) =


    - (16 + 8 + 4 + 2)(10) =


    -30(10)

  • Binary signed number, 1001 1110 = -30(10), signed negative integer in base 10