Signed Binary: Convert and Write Signed Binary Numbers as Decimal System Integer Numbers in Base Ten. Steps and Explanations

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

Binary number's first bit (leftmost) is reserved for the sign: 1 negative, 0 positive.

Binary number's length must be: 2, 4, 8, 16, 32, 64, or else extra bits on 0 are 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.

The latest signed binary numbers converted and written as signed integers in decimal system (in base ten)

Convert the signed binary number 0000 0000 1100 0100 1110 0110 1100 1010 1100 1010 0110 0100 0110 0000 1100 0001, write it as a decimal system integer number (written in base ten) Sep 08 03:14 UTC (GMT)
Convert the signed binary number 0000 0000 0000 0000 0000 0000 0000 0001 0111 0100 0101 0101 1010 1100 1101 0100, write it as a decimal system integer number (written in base ten) Sep 08 03:09 UTC (GMT)
Convert the signed binary number 0000 0100 0000 0010, write it as a decimal system integer number (written in base ten) Sep 08 03:08 UTC (GMT)
Convert the signed binary number 0100 0000 0010 1000 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0011 1001, write it as a decimal system integer number (written in base ten) Sep 08 03:03 UTC (GMT)
Convert the signed binary number 0000 1011, write it as a decimal system integer number (written in base ten) Sep 08 02:53 UTC (GMT)
Convert the signed binary number 1100 0011 0010 0101, write it as a decimal system integer number (written in base ten) Sep 08 02:51 UTC (GMT)
Convert the signed binary number 0000 1011, write it as a decimal system integer number (written in base ten) Sep 08 02:50 UTC (GMT)
Convert the signed binary number 0110 1000 0111 1011, write it as a decimal system integer number (written in base ten) Sep 08 02:46 UTC (GMT)
Convert the signed binary number 0000 0000 0000 0000 0000 0000 0000 1010 1100 1100 1010 1011 0110 1111 1101 0110, write it as a decimal system integer number (written in base ten) Sep 08 02:44 UTC (GMT)
Convert the signed binary number 0000 0000 0000 0000 0000 0000 0000 0000 1001 0010 1110 1001 1000 0000 0011 1000, write it as a decimal system integer number (written in base ten) Sep 08 02:42 UTC (GMT)
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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