Binary 2 Decimal Transforming Numerical Systems

Lesson 2:Binary 2 Decimal

Number we want to transform uses base X: we would like to transform this number into new one, that uses Y base. In this case we will use method of continuous dividing and multiplying (dividing numbers left of comma (,) with Y and multiplying numbers on the right side of comma, by Y - rational numbers). This method is best understood looking at these examples, where X = 2, and Y = 10 (binary and decimal base, B1=2, B2=10):

Binary System:
Base: 2
Digits: 0, 1
Example: 27 (decimal) = 11011 ₂ (binary)

Decimal System:
Base: 10
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Binary 2 Decimal

Example

Transform 110101 (binary) into decimal number

110101 2 = 1*25 + 1*24 + 0*23 + 1*22 + 0*21 + 1*20
 = 1*25 + 1*24 + 1*22 + 1*20
 = 1*32 + 1*16 + 1*4 + 1*1
 = 53 10

Example

Transform -11,101 (binary) into decimal number

-11,101 2 = - (1*21 + 1*20 + 1*2-1 + 0*2-2 + 1*2-3)
 = - (1*21 + 1*20 + 1*2-1 + 1*2-3)
 = - (1*2 + 1*1 + 1*0,5 + 1*0,125)
 = - 3 , 625