# 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)

 1110 1101 1000 1011 = -4,725 Sep 28 10:08 UTC (GMT) 0111 0000 1110 1100 = 28,908 Sep 28 10:08 UTC (GMT) 0110 1101 1001 1000 0000 0000 0000 1010 = 1,838,678,026 Sep 28 10:07 UTC (GMT) 0000 0000 0000 0010 1111 1110 0000 0001 = 196,097 Sep 28 10:07 UTC (GMT) 0000 0000 0101 1010 0010 0000 0101 1011 = 5,906,523 Sep 28 10:06 UTC (GMT) 1000 0001 0011 1111 1111 1111 1111 0101 = -2,126,512,139 Sep 28 10:06 UTC (GMT) 0000 0000 0000 0011 0100 0110 1001 0000 = 214,672 Sep 28 10:06 UTC (GMT) 0010 1100 1001 0111 = 11,415 Sep 28 10:05 UTC (GMT) 1111 0011 1010 1110 = -3,154 Sep 28 10:04 UTC (GMT) 1111 1111 1111 1111 1111 1010 1000 0110 = -1,402 Sep 28 10:04 UTC (GMT) 0100 0010 1110 0100 1000 0000 0000 1101 = 1,122,271,245 Sep 28 10:04 UTC (GMT) 0000 0000 0000 0000 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 0100 = 281,474,976,710,644 Sep 28 10:03 UTC (GMT) 1111 1111 1111 1111 1100 1101 0100 1000 = -12,984 Sep 28 10:02 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: