Signed binary number 1111 1111 1101 0100 0011 1111 1111 1011 converted to an integer in base ten

Signed binary 1111 1111 1101 0100 0011 1111 1111 1011(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.

1111 1111 1101 0100 0011 1111 1111 1011 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:

1111 1111 1101 0100 0011 1111 1111 1011 = 111 1111 1101 0100 0011 1111 1111 1011

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

    • 230

      1

    • 229

      1

    • 228

      1

    • 227

      1

    • 226

      1

    • 225

      1

    • 224

      1

    • 223

      1

    • 222

      1

    • 221

      0

    • 220

      1

    • 219

      0

    • 218

      1

    • 217

      0

    • 216

      0

    • 215

      0

    • 214

      0

    • 213

      1

    • 212

      1

    • 211

      1

    • 210

      1

    • 29

      1

    • 28

      1

    • 27

      1

    • 26

      1

    • 25

      1

    • 24

      1

    • 23

      1

    • 22

      0

    • 21

      1

    • 20

      1

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

111 1111 1101 0100 0011 1111 1111 1011(2) =

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

(1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 0 + 1 048 576 + 0 + 262 144 + 0 + 0 + 0 + 0 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 0 + 2 + 1)(10) =

(1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 1 048 576 + 262 144 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 2 + 1)(10) =

2 144 616 443(10)

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

1111 1111 1101 0100 0011 1111 1111 1011(2) = -2 144 616 443(10)

Number 1111 1111 1101 0100 0011 1111 1111 1011(2) converted from signed binary to an integer in decimal system (in base 10):
1111 1111 1101 0100 0011 1111 1111 1011(2) = -2 144 616 443(10)

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

More operations of this kind:

1111 1111 1101 0100 0011 1111 1111 1010 = ?

1111 1111 1101 0100 0011 1111 1111 1100 = ?


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)

1111 1111 1101 0100 0011 1111 1111 1011 = -2,144,616,443 Mar 03 01:55 UTC (GMT)
1001 1001 0100 0011 = -6,467 Mar 03 01:55 UTC (GMT)
1000 1101 = -13 Mar 03 01:54 UTC (GMT)
1101 0100 0000 0001 = -21,505 Mar 03 01:54 UTC (GMT)
0000 0000 0000 0000 0000 0000 0000 0000 1010 0000 0001 1011 1101 1110 0110 1010 = 2,686,180,970 Mar 03 01:54 UTC (GMT)
0000 0000 0000 1001 1100 0111 1110 0110 1110 1010 0111 0111 1110 0111 0111 0000 = 2,753,069,380,527,984 Mar 03 01:54 UTC (GMT)
0101 0001 0011 1000 = 20,792 Mar 03 01:54 UTC (GMT)
0001 1101 = 29 Mar 03 01:54 UTC (GMT)
0000 0000 0000 0000 1000 1001 1000 0001 = 35,201 Mar 03 01:54 UTC (GMT)
1101 0101 1011 0111 = -21,943 Mar 03 01:53 UTC (GMT)
0000 0010 1011 0101 = 693 Mar 03 01:53 UTC (GMT)
0000 1011 1001 1111 0111 0110 1000 1001 = 194,999,945 Mar 03 01:53 UTC (GMT)
1101 1111 0000 1100 = -24,332 Mar 03 01:53 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