Signed binary one's complement number 0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101 converted to decimal system (base ten) signed integer

How to convert a signed binary one's complement:
0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101(2)
to an integer in decimal system (in base 10)

1. Is this a positive or a negative number?


In a signed binary one's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.

0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101 is the binary representation of a positive integer, on 64 bits (8 Bytes).


2. Get the binary representation of the positive (unsigned) number:


* Run this step only if the number is negative *

Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:

* Not the case *


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

    • 263

      0

    • 262

      0

    • 261

      0

    • 260

      0

    • 259

      0

    • 258

      0

    • 257

      0

    • 256

      0

    • 255

      0

    • 254

      1

    • 253

      0

    • 252

      0

    • 251

      0

    • 250

      0

    • 249

      1

    • 248

      0

    • 247

      1

    • 246

      1

    • 245

      1

    • 244

      1

    • 243

      1

    • 242

      1

    • 241

      0

    • 240

      0

    • 239

      1

    • 238

      1

    • 237

      1

    • 236

      1

    • 235

      1

    • 234

      1

    • 233

      1

    • 232

      1

    • 231

      0

    • 230

      1

    • 229

      1

    • 228

      0

    • 227

      0

    • 226

      0

    • 225

      0

    • 224

      1

    • 223

      1

    • 222

      0

    • 221

      0

    • 220

      1

    • 219

      0

    • 218

      1

    • 217

      1

    • 216

      1

    • 215

      0

    • 214

      0

    • 213

      1

    • 212

      0

    • 211

      0

    • 210

      1

    • 29

      0

    • 28

      0

    • 27

      1

    • 26

      1

    • 25

      0

    • 24

      1

    • 23

      0

    • 22

      1

    • 21

      0

    • 20

      1

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

0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101(2) =

(0 × 263 + 0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 0 × 258 + 0 × 257 + 0 × 256 + 0 × 255 + 1 × 254 + 0 × 253 + 0 × 252 + 0 × 251 + 0 × 250 + 1 × 249 + 0 × 248 + 1 × 247 + 1 × 246 + 1 × 245 + 1 × 244 + 1 × 243 + 1 × 242 + 0 × 241 + 0 × 240 + 1 × 239 + 1 × 238 + 1 × 237 + 1 × 236 + 1 × 235 + 1 × 234 + 1 × 233 + 1 × 232 + 0 × 231 + 1 × 230 + 1 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 0 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 0 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =

(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 18 014 398 509 481 984 + 0 + 0 + 0 + 0 + 562 949 953 421 312 + 0 + 140 737 488 355 328 + 70 368 744 177 664 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 4 398 046 511 104 + 0 + 0 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 0 + 1 073 741 824 + 536 870 912 + 0 + 0 + 0 + 0 + 16 777 216 + 8 388 608 + 0 + 0 + 1 048 576 + 0 + 262 144 + 131 072 + 65 536 + 0 + 0 + 8 192 + 0 + 0 + 1 024 + 0 + 0 + 128 + 64 + 0 + 16 + 0 + 4 + 0 + 1)(10) =

(18 014 398 509 481 984 + 562 949 953 421 312 + 140 737 488 355 328 + 70 368 744 177 664 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 4 398 046 511 104 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 1 073 741 824 + 536 870 912 + 16 777 216 + 8 388 608 + 1 048 576 + 262 144 + 131 072 + 65 536 + 8 192 + 1 024 + 128 + 64 + 16 + 4 + 1)(10) =

18 855 522 247 058 645(10)

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

0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101(2) = 18 855 522 247 058 645(10)

Conclusion:
Number 0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101(2) converted from signed binary one's complement representation to an integer in decimal system (in base 10):

0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101(2) = 18 855 522 247 058 645(10)

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

More operations of this kind:

0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0100 = ?

0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0110 = ?


Convert signed binary one's complement numbers to decimal system (base ten) integers

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 in one's complement representation to an integer in base ten:

1) In a signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive.

2) Construct the unsigned binary number: flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s.

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

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

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

Latest binary numbers in one's complement representation converted to signed integers numbers in decimal system (base ten)

0000 0000 0100 0010 1111 1100 1111 1111 0110 0001 1001 0111 0010 0100 1101 0101 = 18,855,522,247,058,645 Jan 20 13:15 UTC (GMT)
1111 1111 1010 1110 = -81 Jan 20 13:14 UTC (GMT)
1111 0011 0011 0011 = -3,276 Jan 20 13:14 UTC (GMT)
0000 0000 1100 1000 0000 0000 0000 0000 = 13,107,200 Jan 20 13:12 UTC (GMT)
0000 0011 0001 0110 = 790 Jan 20 13:11 UTC (GMT)
0100 1110 0010 1010 = 20,010 Jan 20 13:11 UTC (GMT)
0000 0000 0011 1111 = 63 Jan 20 13:07 UTC (GMT)
1100 0001 1110 0000 0000 0000 0000 1001 = -1,042,284,534 Jan 20 13:06 UTC (GMT)
0000 0001 0111 0100 = 372 Jan 20 13:02 UTC (GMT)
0000 0011 1100 1101 = 973 Jan 20 13:02 UTC (GMT)
0000 0000 0000 0000 0000 0000 0000 0110 = 6 Jan 20 13:00 UTC (GMT)
1000 0000 0111 1101 = -32,642 Jan 20 12:59 UTC (GMT)
0011 1100 1101 0011 1100 1100 1000 1101 = 1,020,513,421 Jan 20 12:58 UTC (GMT)
All the converted signed binary one's complement numbers

How to convert signed binary numbers in one's complement representation from binary system to decimal

To understand how to convert a signed binary number in one's complement representation from binary system to decimal (base ten), the easiest way is to do it through an example - convert binary, 1001 1101, to base ten:

  • In a signed binary one's complement, first bit (leftmost) indicates the sign, 1 = negative, 0 = positive. The first bit is 1, so our number is negative.
  • Get the binary representation of the positive number, flip all the bits in the signed binary one's complement representation (reversing the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
    !(1001 1101) = 0110 0010
  • Write bellow the positive binary number representation 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 by increasing each corresonding power of 2 by exactly one unit:
  • powers of 2: 7 6 5 4 3 2 1 0
    digits: 0 1 1 0 0 0 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:

    0110 0010(2) =

    (0 × 27 + 1 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =

    (0 + 64 + 32 + 0 + 0 + 0 + 2 + 0)(10) =

    (64 + 32 + 2)(10) =

    98(10)

  • Signed binary number in one's complement representation, 1001 1110 = -98(10), a signed negative integer in base 10