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

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

 0000 0000 0000 0000 0000 0000 0001 1111 1111 1111 1111 1111 1111 1111 0101 0000 = 137,438,953,296 Sep 29 14:09 UTC (GMT) 0000 0000 0000 0001 0000 0000 1111 1111 = 65,791 Sep 29 14:08 UTC (GMT) 0000 0000 0000 0001 1111 0110 0000 0010 = 128,514 Sep 29 14:08 UTC (GMT) 0100 1010 0011 1101 0100 0111 1010 1101 = 1,245,530,029 Sep 29 14:08 UTC (GMT) 1110 0001 0001 0000 0000 0000 0000 0001 = -1,628,438,529 Sep 29 14:07 UTC (GMT) 1110 0011 1010 1011 = -25,515 Sep 29 14:07 UTC (GMT) 1001 1001 1001 1001 1001 1001 1010 0000 = -429,496,736 Sep 29 14:05 UTC (GMT) 0000 0001 0110 0011 = 355 Sep 29 14:05 UTC (GMT) 0001 0001 = 17 Sep 29 14:04 UTC (GMT) 0000 0010 0000 0000 = 512 Sep 29 14:04 UTC (GMT) 0011 1100 = 60 Sep 29 14:03 UTC (GMT) 0111 1110 1101 0101 = 32,469 Sep 29 14:02 UTC (GMT) 1111 1111 = -127 Sep 29 14:02 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: