Unsigned: Binary ↘ Integer: 110 1010 1100 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) 110 1010 1100(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.

  • 210

    1

  • 29

    1

  • 28

    0

  • 27

    1

  • 26

    0

  • 25

    1

  • 24

    0

  • 23

    1

  • 22

    1

  • 21

    0

  • 20

    0

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

110 1010 1100(2) =

(1 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20)(10) =

(1 024 + 512 + 0 + 128 + 0 + 32 + 0 + 8 + 4 + 0 + 0)(10) =

(1 024 + 512 + 128 + 32 + 8 + 4)(10) =

1 708(10)

The number 110 1010 1100(2) converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):
110 1010 1100(2) = 1 708(10)

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

More operation with unsigned binary numbers:

» The unsigned binary number 110 1010 1011 (in base two), converted and written as a positive integer (with no sign) in decimal system (in base ten) = ?

» The unsigned binary number 110 1010 1101 (in base two), converted and written as a positive integer (with no sign) in decimal system (in base ten) = ?

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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