One's Complement: Binary ↘ Integer: 0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0011 Signed Binary Number in One's Complement Representation, Converted and Written as a Decimal System Integer (in Base Ten)

Signed binary in one's complement representation 0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0011(2) converted to an integer in decimal system (in base ten) = ?

1. Is this a positive or a negative number?

0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0011 is the binary representation of a positive integer, on 64 bits (8 Bytes).


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


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

* Run this step only if the number is negative *

Flip all the bits of the signed binary in 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 - the number is positive *


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

  • 263

    0
  • 262

    0
  • 261

    1
  • 260

    0
  • 259

    1
  • 258

    1
  • 257

    1
  • 256

    1
  • 255

    0
  • 254

    0
  • 253

    0
  • 252

    1
  • 251

    1
  • 250

    1
  • 249

    1
  • 248

    1
  • 247

    0
  • 246

    0
  • 245

    0
  • 244

    0
  • 243

    0
  • 242

    0
  • 241

    0
  • 240

    1
  • 239

    0
  • 238

    0
  • 237

    0
  • 236

    0
  • 235

    0
  • 234

    0
  • 233

    0
  • 232

    0
  • 231

    0
  • 230

    0
  • 229

    0
  • 228

    0
  • 227

    0
  • 226

    0
  • 225

    0
  • 224

    0
  • 223

    0
  • 222

    0
  • 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

    1
  • 23

    0
  • 22

    0
  • 21

    1
  • 20

    1

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

0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0011(2) =


(0 × 263 + 0 × 262 + 1 × 261 + 0 × 260 + 1 × 259 + 1 × 258 + 1 × 257 + 1 × 256 + 0 × 255 + 0 × 254 + 0 × 253 + 1 × 252 + 1 × 251 + 1 × 250 + 1 × 249 + 1 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 0 × 241 + 1 × 240 + 0 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 0 × 235 + 0 × 234 + 0 × 233 + 0 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 0 × 222 + 0 × 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 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =


(0 + 0 + 2 305 843 009 213 693 952 + 0 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 0 + 0 + 0 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 099 511 627 776 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 16 + 0 + 0 + 2 + 1)(10) =


(2 305 843 009 213 693 952 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 1 099 511 627 776 + 16 + 2 + 1)(10) =


3 395 433 743 572 271 123(10)

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

0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0011(2) = 3 395 433 743 572 271 123(10)

The signed binary number in one's complement representation 0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0011(2) converted and written as an integer in decimal system (base ten):
0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0011(2) = 3 395 433 743 572 271 123(10)

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

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

Convert signed binary number written in one's complement representation 0000 0000 0000 0001 1111 1000 1101 1101 0011 1010 1111 1110 0001 0011 1110 1011, write it as a decimal system (base ten) integer Jun 17 16:14 UTC (GMT)
Convert signed binary number written in one's complement representation 1110 0011, write it as a decimal system (base ten) integer Jun 17 16:13 UTC (GMT)
Convert signed binary number written in one's complement representation 1001 0100 0011 0110, write it as a decimal system (base ten) integer Jun 17 16:13 UTC (GMT)
Convert signed binary number written in one's complement representation 1000 0000 0000 0000 0000 0000 1110 0001, write it as a decimal system (base ten) integer Jun 17 16:12 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1000 0000 0000 1101 1011, write it as a decimal system (base ten) integer Jun 17 16:12 UTC (GMT)
Convert signed binary number written in one's complement representation 1100 0001 0110 1011 1111 1111 1110 1111, write it as a decimal system (base ten) integer Jun 17 16:11 UTC (GMT)
Convert signed binary number written in one's complement representation 0111 1111 1010 0011 1100 0000 0011 1111 1001 1111 1110 1000 1111 0000 0100 1111, write it as a decimal system (base ten) integer Jun 17 16:11 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0111 1101 1111 0110 0001, write it as a decimal system (base ten) integer Jun 17 16:11 UTC (GMT)
Convert signed binary number written in one's complement representation 1011 1000 0110 1000, write it as a decimal system (base ten) integer Jun 17 16:10 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0111 0010 0000, write it as a decimal system (base ten) integer Jun 17 16:10 UTC (GMT)
All the signed binary numbers in one's complement representation converted to decimal system (base ten) integers

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