Signed binary number 1010 1000 0110 1010 0000 1100 0010 1101 converted to an integer in base ten

Signed binary 1010 1000 0110 1010 0000 1100 0010 1101(2) to an integer in decimal system (in base 10) = ?

1. Is this a positive or a negative number?


In a signed binary, first bit (the leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.

1010 1000 0110 1010 0000 1100 0010 1101 is the binary representation of a negative integer, on 32 bits (4 Bytes).


2. Construct the unsigned binary number, exclude the first bit (the leftmost), that is reserved for the sign:

1010 1000 0110 1010 0000 1100 0010 1101 = 010 1000 0110 1010 0000 1100 0010 1101

3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:

    • 230

      0
    • 229

      1
    • 228

      0
    • 227

      1
    • 226

      0
    • 225

      0
    • 224

      0
    • 223

      0
    • 222

      1
    • 221

      1
    • 220

      0
    • 219

      1
    • 218

      0
    • 217

      1
    • 216

      0
    • 215

      0
    • 214

      0
    • 213

      0
    • 212

      0
    • 211

      1
    • 210

      1
    • 29

      0
    • 28

      0
    • 27

      0
    • 26

      0
    • 25

      1
    • 24

      0
    • 23

      1
    • 22

      1
    • 21

      0
    • 20

      1

4. Multiply each bit by its corresponding power of 2 and add all the terms up:

010 1000 0110 1010 0000 1100 0010 1101(2) =


(0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 1 × 222 + 1 × 221 + 0 × 220 + 1 × 219 + 0 × 218 + 1 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 1 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =


(0 + 536 870 912 + 0 + 134 217 728 + 0 + 0 + 0 + 0 + 4 194 304 + 2 097 152 + 0 + 524 288 + 0 + 131 072 + 0 + 0 + 0 + 0 + 0 + 2 048 + 1 024 + 0 + 0 + 0 + 0 + 32 + 0 + 8 + 4 + 0 + 1)(10) =


(536 870 912 + 134 217 728 + 4 194 304 + 2 097 152 + 524 288 + 131 072 + 2 048 + 1 024 + 32 + 8 + 4 + 1)(10) =


678 038 573(10)

5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:

1010 1000 0110 1010 0000 1100 0010 1101(2) = -678 038 573(10)

Number 1010 1000 0110 1010 0000 1100 0010 1101(2) converted from signed binary to an integer in decimal system (in base 10):
1010 1000 0110 1010 0000 1100 0010 1101(2) = -678 038 573(10)

Spaces used to group digits: for binary, by 4; for decimal, by 3.


More operations of this kind:

1010 1000 0110 1010 0000 1100 0010 1100 = ?

1010 1000 0110 1010 0000 1100 0010 1110 = ?


Convert signed binary numbers to integers in decimal system (base 10)

First bit (the leftmost) is reserved for the sign, 1 = negative, 0 = positive. This bit does not count when calculating the absolute value.

Entered binary number length must be: 2, 4, 8, 16, 32, or 64 - otherwise extra bits on 0 will be added in front (to the left).

How to convert a signed binary number to an integer in base ten:

1) Construct the unsigned binary number: exclude the first bit (the leftmost); this bit is reserved for the sign, 1 = negative, 0 = positive and does not count when calculating the absolute value (without sign).

2) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

3) Add all the terms up to get the positive integer number in base ten.

4) Adjust the sign of the integer number by the first bit of the initial binary number.

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

1010 1000 0110 1010 0000 1100 0010 1101 = -678,038,573 May 12 07:11 UTC (GMT)
1010 1100 1110 1110 0000 0000 0000 0100 = -753,795,076 May 12 07:11 UTC (GMT)
0100 0100 1000 0000 0000 0000 0000 0000 = 1,149,239,296 May 12 07:11 UTC (GMT)
1001 0100 = -20 May 12 07:11 UTC (GMT)
0100 0010 1011 0100 0000 0000 0000 0011 = 1,119,092,739 May 12 07:11 UTC (GMT)
0100 1000 1111 1111 = 18,687 May 12 07:10 UTC (GMT)
1101 1110 0101 1000 = -24,152 May 12 07:09 UTC (GMT)
1111 1111 1100 1010 1000 0110 0100 0010 = -2,143,979,074 May 12 07:09 UTC (GMT)
1000 0000 0010 0110 0000 0110 1101 0101 = -2,492,117 May 12 07:09 UTC (GMT)
0110 0110 1011 1100 = 26,300 May 12 07:09 UTC (GMT)
1000 1111 1111 1111 = -4,095 May 12 07:09 UTC (GMT)
0000 0100 0100 0100 0100 0100 0100 1000 = 71,582,792 May 12 07:09 UTC (GMT)
0000 0001 0000 0000 0000 0000 0000 0111 = 16,777,223 May 12 07:09 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:

    1001 1110 =


    - (0 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =


    - (0 + 0 + 16 + 8 + 4 + 2 + 0)(10) =


    - (16 + 8 + 4 + 2)(10) =


    -30(10)

  • Binary signed number, 1001 1110 = -30(10), signed negative integer in base 10