# Signed binary two's complement number 0011 1111 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)

 0011 1111 = 63 Jan 20 12:15 UTC (GMT) 0111 0111 0110 0001 0110 1001 0111 0100 = 2,002,872,692 Jan 20 12:14 UTC (GMT) 0000 0000 0000 0000 0000 0000 0011 1111 1111 1111 1111 1111 1111 1111 1110 1001 = 274,877,906,921 Jan 20 12:14 UTC (GMT) 0000 0000 0001 0010 1101 0110 1001 1011 = 1,234,587 Jan 20 12:14 UTC (GMT) 1011 0110 1011 1001 = -18,759 Jan 20 12:13 UTC (GMT) 0100 1110 0001 1010 = 19,994 Jan 20 12:13 UTC (GMT) 1101 0001 = -47 Jan 20 12:13 UTC (GMT) 1000 1101 = -115 Jan 20 12:13 UTC (GMT) 0000 0010 0000 0000 0000 0000 0000 0000 = 33,554,432 Jan 20 12:13 UTC (GMT) 0111 1111 1111 1111 1100 0111 1100 0000 = 2,147,469,248 Jan 20 12:12 UTC (GMT) 1111 1111 0000 1010 0001 1101 0110 0110 = -16,114,330 Jan 20 12:12 UTC (GMT) 0000 0001 0000 0000 0000 0001 0000 0100 = 16,777,476 Jan 20 12:11 UTC (GMT) 0000 0100 1111 0010 = 1,266 Jan 20 12:11 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: