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Binary Number Addition
⇨The four basic rules of addition of binary number are:
(i) 0 + 1 = 1
(ii) 1 + 0 = 1
(iii) 0 + 0 = 0
(iv) 1 + 1 = 0 (carry 1 in hand)
⇨ If the sum of 2 bits is greater than 1, we need to shift a column
on the left. In decimal system, 1+1= 2. Binary notation of 2 is 10.
So we keep 0 within the 1st column and shift carry 1 to the 2nd
column. Other rules are same as the decimal number system , i.e. we
add from right to left and the carry over gets added to the digits
in the next column.
⇨ Example: Now lets try adding 11 to 13. Binary for 11 is 1011 which
for 13 is 1101.
Binary Decimal
1 0 1 1 1
+ 1 1 0 1 + 1 3
--------------------------
1 1 0 0 0 2
4
--------------------------
⇨ 1st column = 1 + 1 = 10. We keep 0 in 1st column and carry over 1 to 2nd
column.
⇨ 2nd column = 1 + 0 + 1 (carry over) = (1 + 0) + 1 = 1 + 1 = 10. Once again
we keep 0 in 2nd column and carry over 1 to 3rd column.
⇨ 3rd column = 0 + 1 + 1 (carry over) = (0 + 1) + 1 = 1 + 1 = 10. Keep 0 in
3rd column and carry over 1 in 4th column.
⇨ 4th column = 1 + 1 + 1 (carry over) = (1 + 1) + 1 = 10 + 1 = 11. Keep 1 in
4th column and carry over 1 in 5th column. Therefore the sum is 11000.