Base Two to Base Ten: Unsigned Base Two Binary Number 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1011 Converted and Written as a Base Ten Natural Number (Positive Integer, Without Sign), in Decimal System

Unsigned base two binary number 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1011(2) converted and written as a base ten number

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

  • 263

    1

  • 262

    1

  • 261

    0

  • 260

    0

  • 259

    1

  • 258

    1

  • 257

    0

  • 256

    0

  • 255

    1

  • 254

    1

  • 253

    0

  • 252

    0

  • 251

    1

  • 250

    1

  • 249

    0

  • 248

    0

  • 247

    1

  • 246

    1

  • 245

    0

  • 244

    0

  • 243

    1

  • 242

    1

  • 241

    0

  • 240

    0

  • 239

    1

  • 238

    1

  • 237

    0

  • 236

    0

  • 235

    1

  • 234

    1

  • 233

    0

  • 232

    0

  • 231

    1

  • 230

    1

  • 229

    0

  • 228

    0

  • 227

    1

  • 226

    1

  • 225

    0

  • 224

    0

  • 223

    1

  • 222

    1

  • 221

    0

  • 220

    0

  • 219

    1

  • 218

    1

  • 217

    0

  • 216

    0

  • 215

    1

  • 214

    1

  • 213

    0

  • 212

    0

  • 211

    1

  • 210

    1

  • 29

    0

  • 28

    0

  • 27

    1

  • 26

    1

  • 25

    0

  • 24

    0

  • 23

    1

  • 22

    0

  • 21

    1

  • 20

    1

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

1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1011(2) =

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

(9 223 372 036 854 775 808 + 4 611 686 018 427 387 904 + 0 + 0 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 0 + 0 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 0 + 0 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 0 + 0 + 140 737 488 355 328 + 70 368 744 177 664 + 0 + 0 + 8 796 093 022 208 + 4 398 046 511 104 + 0 + 0 + 549 755 813 888 + 274 877 906 944 + 0 + 0 + 34 359 738 368 + 17 179 869 184 + 0 + 0 + 2 147 483 648 + 1 073 741 824 + 0 + 0 + 134 217 728 + 67 108 864 + 0 + 0 + 8 388 608 + 4 194 304 + 0 + 0 + 524 288 + 262 144 + 0 + 0 + 32 768 + 16 384 + 0 + 0 + 2 048 + 1 024 + 0 + 0 + 128 + 64 + 0 + 0 + 8 + 0 + 2 + 1)(10) =

(9 223 372 036 854 775 808 + 4 611 686 018 427 387 904 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 140 737 488 355 328 + 70 368 744 177 664 + 8 796 093 022 208 + 4 398 046 511 104 + 549 755 813 888 + 274 877 906 944 + 34 359 738 368 + 17 179 869 184 + 2 147 483 648 + 1 073 741 824 + 134 217 728 + 67 108 864 + 8 388 608 + 4 194 304 + 524 288 + 262 144 + 32 768 + 16 384 + 2 048 + 1 024 + 128 + 64 + 8 + 2 + 1)(10) =

14 757 395 258 967 641 291(10)

The number 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1011(2) converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):
1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1011(2) = 14 757 395 258 967 641 291(10)

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

» More ops: The unsigned base two binary number 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 1100 converted and written as a base ten positive integer, with no sign, in decimal system

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How to convert unsigned binary numbers from binary system to decimal? Simply convert from base two to base ten.

To understand how to convert a number from base two to base ten, the easiest way is to do it through an example - convert the number from base two, 101 0011(2), to base ten:

  • Write bellow the binary number 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, increasing each corresponding power of 2 by exactly one unit each time we move to the left:
  • powers of 2: 6 5 4 3 2 1 0
    digits: 1 0 1 0 0 1 1
  • 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:

    101 0011(2) =

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

    (64 + 0 + 16 + 0 + 0 + 2 + 1)(10) =

    (64 + 16 + 2 + 1)(10) =

    83(10)

  • Binary unsigned number (base 2), 101 0011(2) = 83(10), unsigned positive integer in base 10