Signed binary two's complement number 1010 converted to decimal system (base ten) signed integer

• 23

0
• 22

1
• 21

1
• 20

0

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

 1010 = -6 Oct 15 03:47 UTC (GMT) 0000 0000 0000 0000 0000 0000 0011 0100 1011 0100 1011 1101 0110 0010 1010 1100 = 226,370,609,836 Oct 15 03:47 UTC (GMT) 1001 1111 = -97 Oct 15 03:47 UTC (GMT) 1000 0010 = -126 Oct 15 03:47 UTC (GMT) 0000 0000 1100 0101 = 197 Oct 15 03:46 UTC (GMT) 0100 0000 1000 0000 0000 0000 0000 0000 = 1,082,130,432 Oct 15 03:45 UTC (GMT) 1011 0010 = -78 Oct 15 03:44 UTC (GMT) 1001 0000 = -112 Oct 15 03:44 UTC (GMT) 1000 0000 0111 1000 = -32,648 Oct 15 03:43 UTC (GMT) 0100 0111 1100 0010 0000 1011 0000 1111 0000 0000 0000 0000 0000 0000 0000 0000 = 5,170,707,481,227,165,696 Oct 15 03:43 UTC (GMT) 0000 0001 1010 1111 = 431 Oct 15 03:43 UTC (GMT) 0001 1001 0111 0010 = 6,514 Oct 15 03:41 UTC (GMT) 0000 0011 1000 1101 = 909 Oct 15 03:41 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: