Simplify (10101+10111)base 2
To simplify the expression (10101 + 10111)base 2, we need to perform binary addition.
1 0 1 0 1
+ 1 0 1 1 1
---------------
1 0 1 0 0 0
Therefore, (10101 + 10111)base 2 simplifies to 101000 in binary form.
To simplify the expression (10101 + 10111) in base 2, you need to perform the binary addition. Just like in decimal addition, you start from the rightmost digit and work your way to the left, carrying over any excess when the sum exceeds the base.
Let's break down the addition step-by-step:
1 0 1 0 1
+ 1 0 1 1 1
-----------
We start by adding the rightmost digits: 1 + 1 = 10. Write down the "0" and carry over the "1" to the next column.
1 0 1 0 1
+ 1 0 1 1 1
-----------
0
Next, we add the second digits from the right, including the carried over value: 1 + 1 + 1 = 11. Write down the "1" and carry over the "1" to the next column.
1 0 1 0 1
+ 1 0 1 1 1
-----------
10
For the third digits from the right, we have 0 + 1 + 1 = 10. Write down the "0" and carry over the "1" to the next column.
1 0 1 0 1
+ 1 0 1 1 1
-----------
010
Moving on to the fourth digits from the right, we have 1 + 0 + 0 = 1. Write down the "1" without any carry over.
1 0 1 0 1
+ 1 0 1 1 1
-----------
1010
Finally, for the leftmost digits, we only have the digit "1" remaining.
1 0 1 0 1
+ 1 0 1 1 1
-----------
10101
Therefore, the simplified result of (10101 + 10111) in base 2 is equal to 10101.