Signed binary one's complement number 0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000 converted to decimal system (base ten) signed integer

Signed binary one's complement 0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000(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.

0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000 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

      1
    • 261

      1
    • 260

      1
    • 259

      0
    • 258

      0
    • 257

      0
    • 256

      0
    • 255

      0
    • 254

      0
    • 253

      0
    • 252

      0
    • 251

      0
    • 250

      0
    • 249

      0
    • 248

      0
    • 247

      0
    • 246

      0
    • 245

      0
    • 244

      0
    • 243

      0
    • 242

      0
    • 241

      0
    • 240

      0
    • 239

      0
    • 238

      0
    • 237

      1
    • 236

      1
    • 235

      1
    • 234

      1
    • 233

      1
    • 232

      1
    • 231

      1
    • 230

      0
    • 229

      0
    • 228

      1
    • 227

      1
    • 226

      1
    • 225

      1
    • 224

      1
    • 223

      1
    • 222

      1
    • 221

      1
    • 220

      0
    • 219

      1
    • 218

      0
    • 217

      0
    • 216

      0
    • 215

      1
    • 214

      1
    • 213

      1
    • 212

      1
    • 211

      0
    • 210

      0
    • 29

      0
    • 28

      0
    • 27

      0
    • 26

      0
    • 25

      0
    • 24

      1
    • 23

      0
    • 22

      0
    • 21

      0
    • 20

      0

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

0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000(2) =


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


(0 + 4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 0 + 0 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 0 + 524 288 + 0 + 0 + 0 + 32 768 + 16 384 + 8 192 + 4 096 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 16 + 0 + 0 + 0 + 0)(10) =


(4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 524 288 + 32 768 + 16 384 + 8 192 + 4 096 + 16)(10) =


8 070 450 805 513 711 632(10)

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

0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000(2) = 8 070 450 805 513 711 632(10)

Number 0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000(2) converted from signed binary one's complement representation to an integer in decimal system (in base 10):
0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000(2) = 8 070 450 805 513 711 632(10)

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


More operations of this kind:

0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0000 1111 = ?

0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0001 = ?


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)

0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 0000 = 8,070,450,805,513,711,632 May 12 09:10 UTC (GMT)
0011 1111 1000 0011 = 16,259 May 12 09:10 UTC (GMT)
1110 1011 1111 0011 1010 0101 0001 0001 = -336,354,030 May 12 09:10 UTC (GMT)
0011 1101 1100 1100 1100 1100 1101 0000 = 1,036,831,952 May 12 09:08 UTC (GMT)
1100 0100 0100 1111 1111 1111 1111 1011 = -1,001,390,084 May 12 09:08 UTC (GMT)
0110 0000 0000 1011 = 24,587 May 12 09:08 UTC (GMT)
1001 0000 1000 0010 = -28,541 May 12 09:08 UTC (GMT)
1000 0011 0110 1011 = -31,892 May 12 09:07 UTC (GMT)
1011 1000 = -71 May 12 09:07 UTC (GMT)
1010 1000 0010 1000 = -22,487 May 12 09:07 UTC (GMT)
0110 0110 0111 1011 = 26,235 May 12 09:07 UTC (GMT)
0010 1001 0011 0001 = 10,545 May 12 09:07 UTC (GMT)
0000 0000 1000 1011 = 139 May 12 09:06 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