# Signed binary number 0000 1000 0010 0111 converted to an integer in base ten

• 214

0
• 213

0
• 212

0
• 211

1
• 210

0
• 29

0
• 28

0
• 27

0
• 26

0
• 25

1
• 24

0
• 23

0
• 22

1
• 21

1
• 20

1

## Latest signed binary numbers converted to signed integers in decimal system (base ten)

 0000 1000 0010 0111 = 2,087 Jun 24 16:25 UTC (GMT) 0111 1111 1111 1111 = 32,767 Jun 24 16:25 UTC (GMT) 1000 0000 0000 0000 0000 0000 0001 0000 = -16 Jun 24 16:25 UTC (GMT) 0000 0011 = 3 Jun 24 16:24 UTC (GMT) 0011 0101 0000 1010 = 13,578 Jun 24 16:23 UTC (GMT) 0100 0111 0011 0000 1101 1001 0000 0000 = 1,194,383,616 Jun 24 16:23 UTC (GMT) 0000 0000 1011 0101 = 181 Jun 24 16:23 UTC (GMT) 0000 0000 0110 1001 = 105 Jun 24 16:20 UTC (GMT) 0000 0000 0000 0000 0000 0000 0101 0101 0101 1100 0011 0100 1011 0010 0110 1001 = 366,619,177,577 Jun 24 16:19 UTC (GMT) 1000 0001 1111 0000 0000 0000 0000 0000 = -32,505,856 Jun 24 16:19 UTC (GMT) 1111 1111 0000 0000 = -32,512 Jun 24 16:18 UTC (GMT) 0000 0000 0000 1000 1101 0111 1010 1111 = 579,503 Jun 24 16:18 UTC (GMT) 0001 0111 = 23 Jun 24 16:16 UTC (GMT) All the converted signed binary numbers to integers in base ten

## How to convert signed binary numbers from binary system to decimal (base ten)

### To understand how to convert a signed binary number from binary system to decimal (base ten), the easiest way is to do it through an example - convert the binary number, 1001 1110, to base ten:

• In a signed binary, the first bit (leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value (value without sign). The first bit is 1, so our number is negative.
• Write bellow the binary number 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 and increasing each corresonding power of 2 by exactly one unit, but ignoring the very first bit (the leftmost, the one representing the sign):
•  powers of 2: 6 5 4 3 2 1 0 digits: 1 0 0 1 1 1 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, but also taking care of the number sign: