# Converter of signed binary two's complement: converting to decimal system (base ten) integer numbers

## Latest binary numbers in two's complement representation converted to signed integers in decimal system (base ten)

 1010 0001 1101 0111 = -24,105 May 18 02:07 UTC (GMT) 1011 0010 1000 1000 = -19,832 May 18 02:07 UTC (GMT) 0000 0000 0000 0000 0000 0000 0001 0001 0101 0011 0001 0010 0011 0111 0111 1100 = 74,408,146,812 May 18 02:06 UTC (GMT) 1111 1111 1111 1111 1111 1111 1111 1111 1111 1110 0111 1001 1101 1001 0001 1101 = -25,568,995 May 18 02:06 UTC (GMT) 0100 0001 1101 0000 1111 1111 1111 1101 = 1,104,216,061 May 18 02:06 UTC (GMT) 1011 0011 = -77 May 18 02:06 UTC (GMT) 0011 1100 = 60 May 18 02:05 UTC (GMT) 0011 1001 1011 0000 = 14,768 May 18 02:05 UTC (GMT) 0000 0000 0110 1000 0110 1000 0010 0010 1010 0110 0110 1000 0010 0110 1001 1011 = 29,387,895,607,928,475 May 18 02:05 UTC (GMT) 1000 1000 1100 1010 0110 1011 1111 1010 = -2,000,000,006 May 18 02:05 UTC (GMT) 1011 0010 1010 1001 = -19,799 May 18 02:05 UTC (GMT) 0000 1000 0000 0000 0000 0000 0011 1111 1111 1111 1111 1111 1111 1111 1111 1000 = 576,461,027,181,330,424 May 18 02:05 UTC (GMT) 0101 1100 1000 1010 = 23,690 May 18 02:05 UTC (GMT) All the converted signed binary two's complement numbers

## How to convert signed binary numbers in two's complement representation from binary system to decimal

### To understand how to convert a signed binary number in two's complement representation from the binary system to decimal (base ten), the easiest way is to do it by an example - convert binary, 1101 1110, to base ten:

• In a signed binary two's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
• Get the signed binary representation in one's complement, subtract 1 from the initial number:
1101 1110 - 1 = 1101 1101
• Get the binary representation of the positive number, flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1101 1101) = 0010 0010
• Write bellow the positive binary number representation 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, increasing each corresonding power of 2 by exactly one unit:
•  powers of 2: 7 6 5 4 3 2 1 0 digits: 0 0 1 0 0 0 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: