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 r^{n } + d_{n-1 }x r^{n-1 }+ ......................+ d_{1} x r^{1} + d_{0} x r^{0}
= 2x 8^{2} + 5x 8^{1} +x4x 8^{0}
= 128 + 40 + 4 + = 172
Therefore 245_{8} = 172_{10}.
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