# Signed binary two's complement number 1000 1101 1101 0001 converted to decimal system (base ten) signed integer

• 215

0
• 214

1
• 213

1
• 212

1
• 211

0
• 210

0
• 29

1
• 28

0
• 27

0
• 26

0
• 25

1
• 24

0
• 23

1
• 22

1
• 21

1
• 20

1

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

 1000 1101 1101 0001 = -29,231 Oct 28 11:26 UTC (GMT) 1100 1101 0110 0111 = -12,953 Oct 28 11:26 UTC (GMT) 1010 0101 1001 1010 = -23,142 Oct 28 11:26 UTC (GMT) 1000 1010 0101 1100 = -30,116 Oct 28 11:26 UTC (GMT) 0010 0110 1000 1011 0010 1111 1111 1101 = 646,655,997 Oct 28 11:25 UTC (GMT) 0101 0101 1011 0000 = 21,936 Oct 28 11:25 UTC (GMT) 1100 0111 = -57 Oct 28 11:25 UTC (GMT) 1110 1111 0001 0001 = -4,335 Oct 28 11:24 UTC (GMT) 0000 0001 1011 1000 = 440 Oct 28 11:24 UTC (GMT) 0100 1000 0101 1000 = 18,520 Oct 28 11:24 UTC (GMT) 0001 1010 1010 0111 = 6,823 Oct 28 11:24 UTC (GMT) 1111 1111 1111 1111 1111 1101 0110 1010 = -662 Oct 28 11:24 UTC (GMT) 1101 1110 1010 0011 0100 1111 0000 1110 1101 1110 1101 1011 0001 0100 1010 1111 = -2,403,990,850,798,676,817 Oct 28 11:23 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: