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)

0000 1100 0101 1101 = 3,165 Apr 14 11:14 UTC (GMT)
1111 0110 0111 1011 1101 0100 1111 0011 = -1,987,826,931 Apr 14 11:14 UTC (GMT)
0000 0000 0000 0000 0000 0000 0000 0001 0110 1100 0001 1000 0000 0000 0000 1110 = 6,108,479,502 Apr 14 11:14 UTC (GMT)
1100 0010 1010 1000 1011 1111 1111 0011 = -1,118,355,443 Apr 14 11:14 UTC (GMT)
0000 0000 0011 1111 1111 1100 0111 1011 = 4,193,403 Apr 14 11:13 UTC (GMT)
1111 0011 0101 0010 = -29,522 Apr 14 11:13 UTC (GMT)
1000 0000 0000 0000 0000 0010 0100 0001 = -577 Apr 14 11:13 UTC (GMT)
1011 1100 1111 1111 1111 1111 1111 1111 = -1,023,410,175 Apr 14 11:13 UTC (GMT)
0011 1011 = 59 Apr 14 11:13 UTC (GMT)
1110 0110 0001 1011 = -26,139 Apr 14 11:13 UTC (GMT)
1100 1000 0000 1010 1011 1110 0000 1001 = -1,208,663,561 Apr 14 11:13 UTC (GMT)
0000 0001 0001 1101 = 285 Apr 14 11:13 UTC (GMT)
1101 1100 0001 1011 = -23,579 Apr 14 11:13 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