One's Complement: Binary ↘ Integer: 0010 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 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 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 0011(2) converted to an integer in decimal system (in base ten) = ?

1. Is this a positive or a negative number?

0010 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 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

    0

  • 258

    1

  • 257

    0

  • 256

    1

  • 255

    0

  • 254

    1

  • 253

    0

  • 252

    1

  • 251

    0

  • 250

    0

  • 249

    1

  • 248

    0

  • 247

    1

  • 246

    0

  • 245

    1

  • 244

    0

  • 243

    0

  • 242

    1

  • 241

    0

  • 240

    1

  • 239

    0

  • 238

    1

  • 237

    0

  • 236

    0

  • 235

    0

  • 234

    1

  • 233

    0

  • 232

    1

  • 231

    0

  • 230

    1

  • 229

    0

  • 228

    1

  • 227

    0

  • 226

    0

  • 225

    1

  • 224

    0

  • 223

    0

  • 222

    1

  • 221

    0

  • 220

    1

  • 219

    0

  • 218

    0

  • 217

    1

  • 216

    0

  • 215

    1

  • 214

    0

  • 213

    0

  • 212

    1

  • 211

    0

  • 210

    1

  • 29

    0

  • 28

    0

  • 27

    1

  • 26

    0

  • 25

    1

  • 24

    0

  • 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 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 0011(2) =

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

(0 + 0 + 2 305 843 009 213 693 952 + 0 + 0 + 288 230 376 151 711 744 + 0 + 72 057 594 037 927 936 + 0 + 18 014 398 509 481 984 + 0 + 4 503 599 627 370 496 + 0 + 0 + 562 949 953 421 312 + 0 + 140 737 488 355 328 + 0 + 35 184 372 088 832 + 0 + 0 + 4 398 046 511 104 + 0 + 1 099 511 627 776 + 0 + 274 877 906 944 + 0 + 0 + 0 + 17 179 869 184 + 0 + 4 294 967 296 + 0 + 1 073 741 824 + 0 + 268 435 456 + 0 + 0 + 33 554 432 + 0 + 0 + 4 194 304 + 0 + 1 048 576 + 0 + 0 + 131 072 + 0 + 32 768 + 0 + 0 + 4 096 + 0 + 1 024 + 0 + 0 + 128 + 0 + 32 + 0 + 0 + 0 + 2 + 1)(10) =

(2 305 843 009 213 693 952 + 288 230 376 151 711 744 + 72 057 594 037 927 936 + 18 014 398 509 481 984 + 4 503 599 627 370 496 + 562 949 953 421 312 + 140 737 488 355 328 + 35 184 372 088 832 + 4 398 046 511 104 + 1 099 511 627 776 + 274 877 906 944 + 17 179 869 184 + 4 294 967 296 + 1 073 741 824 + 268 435 456 + 33 554 432 + 4 194 304 + 1 048 576 + 131 072 + 32 768 + 4 096 + 1 024 + 128 + 32 + 2 + 1)(10) =

2 689 393 644 646 077 603(10)

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

0010 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 0011(2) = 2 689 393 644 646 077 603(10)

The signed binary number in one's complement representation 0010 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 0011(2) converted and written as an integer in decimal system (base ten):
0010 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 0011(2) = 2 689 393 644 646 077 603(10)

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

More operations on signed binary in one's complement representation:

» The signed binary in one's complement representation 0010 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 0010 converted and written as an integer number in decimal system (in base ten) = ?

» The signed binary in one's complement representation 0010 0101 0101 0010 1010 0101 0100 0101 0101 0010 0101 0010 1001 0100 1010 0100 converted and written as an integer number in decimal system (in base ten) = ?

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 1001 0000 1000 1010 0101 0001 1001 1010, write it as a decimal system (base ten) integer Sep 14 01:24 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0000 0000 0000 0000 0111 1111 1110 0000 0000 0000 0000 0100 0101, write it as a decimal system (base ten) integer Sep 14 01:24 UTC (GMT)
Convert signed binary number written in one's complement representation 0100 1110 0100 1010, write it as a decimal system (base ten) integer Sep 14 01:23 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0011 1111 1011 0101 1110, write it as a decimal system (base ten) integer Sep 14 01:23 UTC (GMT)
Convert signed binary number written in one's complement representation 0011 0110 1011 0000, write it as a decimal system (base ten) integer Sep 14 01:23 UTC (GMT)
Convert signed binary number written in one's complement representation 1010 0010 1011 1011, write it as a decimal system (base ten) integer Sep 14 01:22 UTC (GMT)
Convert signed binary number written in one's complement representation 0010 1110 0010 1010 0110 0100 0001 0111, write it as a decimal system (base ten) integer Sep 14 01:22 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0110, write it as a decimal system (base ten) integer Sep 14 01:22 UTC (GMT)
Convert signed binary number written in one's complement representation 1011 0110 1100 1101, write it as a decimal system (base ten) integer Sep 14 01:21 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 0000 1111 1111 1110 1011, write it as a decimal system (base ten) integer Sep 14 01:21 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