Unsigned binary number (base two) 1000 1010 1100 0111 0010 0011 0000 0100 1000 1001 1110 1000 0000 0000 0000 1000 converted to decimal system (base ten) positive integer

How to convert an unsigned binary (base 2):
1000 1010 1100 0111 0010 0011 0000 0100 1000 1001 1110 1000 0000 0000 0000 1000(2)
to a positive integer (no sign) in decimal system (in base 10)

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

    • 263

      1
    • 262

      0
    • 261

      0
    • 260

      0
    • 259

      1
    • 258

      0
    • 257

      1
    • 256

      0
    • 255

      1
    • 254

      1
    • 253

      0
    • 252

      0
    • 251

      0
    • 250

      1
    • 249

      1
    • 248

      1
    • 247

      0
    • 246

      0
    • 245

      1
    • 244

      0
    • 243

      0
    • 242

      0
    • 241

      1
    • 240

      1
    • 239

      0
    • 238

      0
    • 237

      0
    • 236

      0
    • 235

      0
    • 234

      1
    • 233

      0
    • 232

      0
    • 231

      1
    • 230

      0
    • 229

      0
    • 228

      0
    • 227

      1
    • 226

      0
    • 225

      0
    • 224

      1
    • 223

      1
    • 222

      1
    • 221

      1
    • 220

      0
    • 219

      1
    • 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

      0
    • 23

      1
    • 22

      0
    • 21

      0
    • 20

      0

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

1000 1010 1100 0111 0010 0011 0000 0100 1000 1001 1110 1000 0000 0000 0000 1000(2) =


(1 × 263 + 0 × 262 + 0 × 261 + 0 × 260 + 1 × 259 + 0 × 258 + 1 × 257 + 0 × 256 + 1 × 255 + 1 × 254 + 0 × 253 + 0 × 252 + 0 × 251 + 1 × 250 + 1 × 249 + 1 × 248 + 0 × 247 + 0 × 246 + 1 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 1 × 241 + 1 × 240 + 0 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 0 × 235 + 1 × 234 + 0 × 233 + 0 × 232 + 1 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 0 × 220 + 1 × 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 + 0 × 20)(10) =


(9 223 372 036 854 775 808 + 0 + 0 + 0 + 576 460 752 303 423 488 + 0 + 144 115 188 075 855 872 + 0 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 0 + 0 + 0 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 0 + 0 + 35 184 372 088 832 + 0 + 0 + 0 + 2 199 023 255 552 + 1 099 511 627 776 + 0 + 0 + 0 + 0 + 0 + 17 179 869 184 + 0 + 0 + 2 147 483 648 + 0 + 0 + 0 + 134 217 728 + 0 + 0 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 0 + 524 288 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 + 0 + 0 + 0)(10) =


(9 223 372 036 854 775 808 + 576 460 752 303 423 488 + 144 115 188 075 855 872 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 35 184 372 088 832 + 2 199 023 255 552 + 1 099 511 627 776 + 17 179 869 184 + 2 147 483 648 + 134 217 728 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 524 288 + 8)(10) =


10 000 000 000 000 000 008(10)

Conclusion:

Number 1000 1010 1100 0111 0010 0011 0000 0100 1000 1001 1110 1000 0000 0000 0000 1000(2) converted from unsigned binary (base 2) to positive integer (no sign) in decimal system (in base 10):


1000 1010 1100 0111 0010 0011 0000 0100 1000 1001 1110 1000 0000 0000 0000 1000(2) = 10 000 000 000 000 000 008(10)

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

Convert unsigned binary numbers (base two) to positive integers in the decimal system (base ten)

How to convert an unsigned binary number (base two) to a positive integer in base ten:

1) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.

2) Add all the terms up to get the integer number in base ten.

Latest unsigned binary numbers converted to positive integers in decimal system (base ten)

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