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 = dn x rn + dn-1 x rn-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