Convert Base Two (2) Number 101 0111 0110 to Base Ten (10): The Unsigned Binary Number Converted to a Positive Integer, Written in the Decimal System. Two Simple Steps, Easy To Follow

The unsigned binary number 101 0111 0101 (in base two), converted and written as a positive integer (with no sign) in decimal system (in base ten) = ?

The unsigned binary number 101 0111 0111 (in base two), converted and written as a positive integer (with no sign) in decimal system (in 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.

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

Conversions Between Decimal System Numbers (Written in Base Ten) and Binary System Numbers (Base Two and Computer Representation):

1. Integer -> Binary

• 1.1. Unsigned integer -> Unsigned binary

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  1.2. Signed integer -> Signed binary

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  1.3. Signed integer -> Signed binary one's complement

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  1.4. Signed integer -> Signed binary two's complement

2. Decimal -> Binary

• 2.1. Decimal -> 32bit single precision IEEE 754 binary floating point

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  2.2. Decimal -> 64bit double precision IEEE 754 binary floating point

3. Binary -> Integer

• 3.1. Unsigned binary -> Unsigned integer

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  3.2. Signed binary -> Signed integer

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  3.3. Signed binary one's complement -> Signed integer

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  3.4. Signed binary two's complement -> Signed integer

4. Binary -> Decimal

• 4.1. 32bit single precision IEEE 754 binary floating point -> Float

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  4.2. 64bit double precision IEEE 754 binary floating point -> Double