any number system to decimal conversion to

Question

Any number System  to Decimal Conversion

To convert a number in any number system to its  equivalent  decimal number, simply multiple each  digit of the number  with its  positional value.

Example :  convert 2548  to decimal.

Solution :  D = d_n  x rⁿ  +  d_n-1 x r^n-1 + ......................+ d₁ x r¹ + d₀ x r⁰

=   2x 8² + 5x 8¹ +x4x 8⁰

= 128 + 40 + 4 + = 172

Therefore  245₈ = 172₁₀.

Binary Arithmetic

Binary Additions'

When  two binary  digits  are added followings  rules  are followed

Rules  for addition  of two  bits.

0 +0= 0

0 +1 = 1

1 + 0= 1

 1 +1 = 1 , 0 which  is equivalent to 2 in  decimal. Here 0 is the sum  and 1 is  carry which  will be  added to the  sum of   adjacent bits.

Example :  Add  10012 and 01012.

Solution :  carry

                       1

              1 0 0 1

             0  1 0 1

            1 1 1  0