# Signed binary two's complement number 1101 0010 converted to decimal system (base ten) signed integer

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

 1101 0010 = -46 Oct 28 10:58 UTC (GMT) 0101 0101 1010 1001 = 21,929 Oct 28 10:58 UTC (GMT) 0011 1000 0010 0110 0000 1100 1011 0010 = 942,017,714 Oct 28 10:58 UTC (GMT) 0010 1100 1110 0111 = 11,495 Oct 28 10:58 UTC (GMT) 0000 0000 0000 0010 1111 1111 1111 1110 = 196,606 Oct 28 10:58 UTC (GMT) 0110 0110 0100 0101 = 26,181 Oct 28 10:58 UTC (GMT) 1110 0110 0001 0110 = -6,634 Oct 28 10:58 UTC (GMT) 0001 1010 1011 1011 = 6,843 Oct 28 10:57 UTC (GMT) 1000 0100 1001 0111 = -31,593 Oct 28 10:57 UTC (GMT) 1010 1010 1010 1010 1010 1010 1010 0101 0110 1010 1001 0101 0101 0101 0101 1110 = -6,148,914,713,786,493,602 Oct 28 10:57 UTC (GMT) 0100 0000 1011 0110 1000 0000 0000 1001 = 1,085,702,153 Oct 28 10:56 UTC (GMT) 1110 1010 1000 1000 = -5,496 Oct 28 10:56 UTC (GMT) 0001 1110 0100 0110 = 7,750 Oct 28 10:56 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: