Unsigned: Binary -> Integer: 10 0000 0100 0001 0000 1000 0100 0011 0010 Convert Base Two (2) Number to Base Ten (10), The Unsigned Binary Converted to a Positive Integer, Written in the Decimal System

The unsigned binary (in base two) 10 0000 0100 0001 0000 1000 0100 0011 0010(2) to a positive integer (with no sign) in decimal system (in base ten) = ?

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

  • 233

    1
  • 232

    0
  • 231

    0
  • 230

    0
  • 229

    0
  • 228

    0
  • 227

    0
  • 226

    1
  • 225

    0
  • 224

    0
  • 223

    0
  • 222

    0
  • 221

    0
  • 220

    1
  • 219

    0
  • 218

    0
  • 217

    0
  • 216

    0
  • 215

    1
  • 214

    0
  • 213

    0
  • 212

    0
  • 211

    0
  • 210

    1
  • 29

    0
  • 28

    0
  • 27

    0
  • 26

    0
  • 25

    1
  • 24

    1
  • 23

    0
  • 22

    0
  • 21

    1
  • 20

    0

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

10 0000 0100 0001 0000 1000 0100 0011 0010(2) =


(1 × 233 + 0 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 1 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 1 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =


(8 589 934 592 + 0 + 0 + 0 + 0 + 0 + 0 + 67 108 864 + 0 + 0 + 0 + 0 + 0 + 1 048 576 + 0 + 0 + 0 + 0 + 32 768 + 0 + 0 + 0 + 0 + 1 024 + 0 + 0 + 0 + 0 + 32 + 16 + 0 + 0 + 2 + 0)(10) =


(8 589 934 592 + 67 108 864 + 1 048 576 + 32 768 + 1 024 + 32 + 16 + 2)(10) =


8 658 125 874(10)

The number 10 0000 0100 0001 0000 1000 0100 0011 0010(2) converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):
10 0000 0100 0001 0000 1000 0100 0011 0010(2) = 8 658 125 874(10)

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

The latest unsigned binary numbers converted and written as positive integers in decimal system (in base ten)

Convert the unsigned binary number written in base two, 10 0000 0100 0001 0000 1000 0100 0011 0010, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 101 0100 1010 0101 0100 1010 0101 0010 0111 1111 1111 1111 1111 1111 1111 1110, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 110 1000 0000 0000 0000 0010 1011 0000, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 10 0001 0000 1000 0000 0010 0000, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 1 0000 0010 0011 0101 0000, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 100 1001 0110 0010 1111 1010 1000, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 1110 1111 1111 1111 1111 1110 1110, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 11 0011 0011 0011 0011 0011 0011 0011 0011 0011 0111 0100, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:46 UTC (GMT)
Convert the unsigned binary number written in base two, 1011 1111 0110 0000 0000 0000 0101 0110, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:45 UTC (GMT)
Convert the unsigned binary number written in base two, 100 0011 1011 1110 1100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0100, write it as a decimal system (written in base ten) positive integer number (whole number) Feb 27 04:45 UTC (GMT)
All the unsigned binary numbers written in base two converted to base ten decimal numbers (as positive integers, or whole numbers)

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