Signed binary number 1010 1011 1111 1111 1111 1111 1111 1100 converted to an integer in base ten

Signed binary 1010 1011 1111 1111 1111 1111 1111 1100(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 1011 1111 1111 1111 1111 1111 1100 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 1011 1111 1111 1111 1111 1111 1100 = 010 1011 1111 1111 1111 1111 1111 1100

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

      1
    • 224

      1
    • 223

      1
    • 222

      1
    • 221

      1
    • 220

      1
    • 219

      1
    • 218

      1
    • 217

      1
    • 216

      1
    • 215

      1
    • 214

      1
    • 213

      1
    • 212

      1
    • 211

      1
    • 210

      1
    • 29

      1
    • 28

      1
    • 27

      1
    • 26

      1
    • 25

      1
    • 24

      1
    • 23

      1
    • 22

      1
    • 21

      0
    • 20

      0

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

010 1011 1111 1111 1111 1111 1111 1100(2) =


(0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 1 × 214 + 1 × 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 + 0 × 20)(10) =


(0 + 536 870 912 + 0 + 134 217 728 + 0 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 0 + 0)(10) =


(536 870 912 + 134 217 728 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4)(10) =


738 197 500(10)

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

1010 1011 1111 1111 1111 1111 1111 1100(2) = -738 197 500(10)

Number 1010 1011 1111 1111 1111 1111 1111 1100(2) converted from signed binary to an integer in decimal system (in base 10):
1010 1011 1111 1111 1111 1111 1111 1100(2) = -738 197 500(10)

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


More operations of this kind:

1010 1011 1111 1111 1111 1111 1111 1011 = ?

1010 1011 1111 1111 1111 1111 1111 1101 = ?


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 1011 1111 1111 1111 1111 1111 1100 = -738,197,500 Feb 27 04:19 UTC (GMT)
1111 1111 1001 1001 1001 1001 1001 1001 1001 1001 1001 1010 0000 0000 0000 0000 = -9,194,548,999,239,630,848 Feb 27 04:19 UTC (GMT)
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1100 0101 0101 1110 1011 1001 = -9,223,372,036,850,933,433 Feb 27 04:19 UTC (GMT)
0100 0000 1000 0111 = 16,519 Feb 27 04:19 UTC (GMT)
1100 0001 1010 0110 1101 1111 1111 1000 = -1,101,455,352 Feb 27 04:19 UTC (GMT)
1001 0001 1110 1110 0000 1110 1000 0101 = -300,813,957 Feb 27 04:18 UTC (GMT)
0110 0100 1110 1010 = 25,834 Feb 27 04:18 UTC (GMT)
0110 0100 1110 1010 = 25,834 Feb 27 04:18 UTC (GMT)
0011 0010 0010 1111 = 12,847 Feb 27 04:18 UTC (GMT)
0100 1001 0111 0100 0010 0000 0011 1001 = 1,232,347,193 Feb 27 04:18 UTC (GMT)
0100 0110 1111 1101 1011 1111 1111 1100 = 1,191,034,876 Feb 27 04:18 UTC (GMT)
0011 0011 0011 1010 = 13,114 Feb 27 04:18 UTC (GMT)
0110 0100 1110 1010 = 25,834 Feb 27 04:18 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