Signed binary number 1011 1110 1110 0000 0000 0000 0000 0000 converted to an integer in base ten

Signed binary 1011 1110 1110 0000 0000 0000 0000 0000(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.

1011 1110 1110 0000 0000 0000 0000 0000 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:

1011 1110 1110 0000 0000 0000 0000 0000 = 011 1110 1110 0000 0000 0000 0000 0000

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

    • 230

      0
    • 229

      1
    • 228

      1
    • 227

      1
    • 226

      1
    • 225

      1
    • 224

      0
    • 223

      1
    • 222

      1
    • 221

      1
    • 220

      0
    • 219

      0
    • 218

      0
    • 217

      0
    • 216

      0
    • 215

      0
    • 214

      0
    • 213

      0
    • 212

      0
    • 211

      0
    • 210

      0
    • 29

      0
    • 28

      0
    • 27

      0
    • 26

      0
    • 25

      0
    • 24

      0
    • 23

      0
    • 22

      0
    • 21

      0
    • 20

      0

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

011 1110 1110 0000 0000 0000 0000 0000(2) =


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


(0 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 0 + 8 388 608 + 4 194 304 + 2 097 152 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0)(10) =


(536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 8 388 608 + 4 194 304 + 2 097 152)(10) =


1 054 867 456(10)

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

1011 1110 1110 0000 0000 0000 0000 0000(2) = -1 054 867 456(10)

Number 1011 1110 1110 0000 0000 0000 0000 0000(2) converted from signed binary to an integer in decimal system (in base 10):
1011 1110 1110 0000 0000 0000 0000 0000(2) = -1 054 867 456(10)

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


More operations of this kind:

1011 1110 1101 1111 1111 1111 1111 1111 = ?

1011 1110 1110 0000 0000 0000 0000 0001 = ?


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)

1011 1110 1110 0000 0000 0000 0000 0000 = -1,054,867,456 Mar 05 07:10 UTC (GMT)
0000 1100 1100 0000 = 3,264 Mar 05 07:10 UTC (GMT)
1000 0001 0010 0100 0100 0111 0111 1100 = -19,154,812 Mar 05 07:09 UTC (GMT)
1000 1001 1110 0111 0000 1001 0001 1101 = -166,136,093 Mar 05 07:09 UTC (GMT)
0111 1101 = 125 Mar 05 07:09 UTC (GMT)
1000 1101 0001 0000 = -3,344 Mar 05 07:09 UTC (GMT)
1111 1000 1001 0011 = -30,867 Mar 05 07:09 UTC (GMT)
1111 0100 1110 0001 = -29,921 Mar 05 07:09 UTC (GMT)
0000 0100 0000 0000 0000 0000 0001 1011 = 67,108,891 Mar 05 07:09 UTC (GMT)
1000 0011 1111 1000 = -1,016 Mar 05 07:09 UTC (GMT)
1011 0001 1110 1110 0010 0100 0000 1111 = -837,690,383 Mar 05 07:08 UTC (GMT)
0011 1110 1001 1011 0100 0000 0000 0000 0000 0001 1101 0101 1011 1111 0111 0100 = 4,511,269,820,516,646,772 Mar 05 07:08 UTC (GMT)
0100 0011 0000 0101 = 17,157 Mar 05 07:08 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