One's Complement: Binary -> Integer: 0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0101 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 0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0101(2) converted to an integer in decimal system (in base ten) = ?

1. Is this a positive or a negative number?

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

0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 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 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

      0

    • 260

      0

    • 259

      0

    • 258

      0

    • 257

      0

    • 256

      0

    • 255

      1

    • 254

      0

    • 253

      0

    • 252

      0

    • 251

      1

    • 250

      0

    • 249

      0

    • 248

      0

    • 247

      1

    • 246

      1

    • 245

      0

    • 244

      1

    • 243

      1

    • 242

      0

    • 241

      0

    • 240

      0

    • 239

      1

    • 238

      1

    • 237

      1

    • 236

      1

    • 235

      0

    • 234

      0

    • 233

      1

    • 232

      0

    • 231

      1

    • 230

      1

    • 229

      0

    • 228

      0

    • 227

      0

    • 226

      0

    • 225

      1

    • 224

      0

    • 223

      0

    • 222

      1

    • 221

      0

    • 220

      0

    • 219

      0

    • 218

      0

    • 217

      0

    • 216

      0

    • 215

      1

    • 214

      1

    • 213

      1

    • 212

      0

    • 211

      1

    • 210

      0

    • 29

      0

    • 28

      0

    • 27

      1

    • 26

      0

    • 25

      0

    • 24

      0

    • 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 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0101(2) =

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

(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 36 028 797 018 963 968 + 0 + 0 + 0 + 2 251 799 813 685 248 + 0 + 0 + 0 + 140 737 488 355 328 + 70 368 744 177 664 + 0 + 17 592 186 044 416 + 8 796 093 022 208 + 0 + 0 + 0 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 0 + 0 + 8 589 934 592 + 0 + 2 147 483 648 + 1 073 741 824 + 0 + 0 + 0 + 0 + 33 554 432 + 0 + 0 + 4 194 304 + 0 + 0 + 0 + 0 + 0 + 0 + 32 768 + 16 384 + 8 192 + 0 + 2 048 + 0 + 0 + 0 + 128 + 0 + 0 + 0 + 0 + 4 + 0 + 1)(10) =

(36 028 797 018 963 968 + 2 251 799 813 685 248 + 140 737 488 355 328 + 70 368 744 177 664 + 17 592 186 044 416 + 8 796 093 022 208 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 8 589 934 592 + 2 147 483 648 + 1 073 741 824 + 33 554 432 + 4 194 304 + 32 768 + 16 384 + 8 192 + 2 048 + 128 + 4 + 1)(10) =

38 519 133 985 368 197(10)

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

0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0101(2) = 38 519 133 985 368 197(10)

The signed binary number in one's complement representation 0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0101(2) converted and written as an integer in decimal system (base ten):
0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0101(2) = 38 519 133 985 368 197(10)

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

The signed binary in one's complement representation 0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0100 converted and written as an integer number in decimal system (in base ten) = ?

The signed binary in one's complement representation 0000 0000 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0110 converted and written as an integer number in decimal system (in base ten) = ?

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

Binary number's length must be: 2, 4, 8, 16, 32, 64 - or else extra bits on 0 are 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.

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 1000 1000 1101 1000 1111 0010 1100 0010 0100 0000 1110 1000 1000 0101, write it as a decimal system (base ten) integer Nov 28 08:40 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0111 1110 1101, write it as a decimal system (base ten) integer Nov 28 08:39 UTC (GMT)
Convert signed binary number written in one's complement representation 0001 0101 1001 0011, write it as a decimal system (base ten) integer Nov 28 08:39 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 1101 1000 0101, write it as a decimal system (base ten) integer Nov 28 08:39 UTC (GMT)
Convert signed binary number written in one's complement representation 0011 1101 1011 1110, write it as a decimal system (base ten) integer Nov 28 08:39 UTC (GMT)
Convert signed binary number written in one's complement representation 1111 1111 1111 1111 1111 0111 1001 0001, write it as a decimal system (base ten) integer Nov 28 08:38 UTC (GMT)
Convert signed binary number written in one's complement representation 1011 1001, write it as a decimal system (base ten) integer Nov 28 08:37 UTC (GMT)
Convert signed binary number written in one's complement representation 1011 0100 1111 1001 0110 0000 0000 0110, write it as a decimal system (base ten) integer Nov 28 08:36 UTC (GMT)
Convert signed binary number written in one's complement representation 0100 0011 0100 1111 0100 1101 0101 0100, write it as a decimal system (base ten) integer Nov 28 08:35 UTC (GMT)
Convert signed binary number written in one's complement representation 0001 0111 1110 0101, write it as a decimal system (base ten) integer Nov 28 08:35 UTC (GMT)
Convert signed binary number written in one's complement representation 0000 0000 0000 1111 1111 1111 1111 1001, write it as a decimal system (base ten) integer Nov 28 08:35 UTC (GMT)
Convert signed binary number written in one's complement representation 1111 1111 1111 1111 1111 0001 1000 1010, write it as a decimal system (base ten) integer Nov 28 08:35 UTC (GMT)
Convert signed binary number written in one's complement representation 1101 0101 0100 0011, write it as a decimal system (base ten) integer Nov 28 08:31 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