Binary Addition Example

1. Find addition of `(11011)_2` and `(1010)_2`

Solution:

Solution is

Step-1 :
`=1_2+0_2`
`=1_10+0_10`
`=1_10`
`=1_2`
`:.` Sum`=1`

Step-2 :
`=1_2+1_2`
`=1_10+1_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

Step-3 :
`=1+0_2+0_2`
`=1+0_10+0_10`
`=1_10`
`=1_2`
`:.` Sum`=1`

Step-4 :
`=1_2+1_2`
`=1_10+1_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

Step-5 :
`=1+1_2+0_2`
`=1+1_10+0_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

2. Find addition of `(11001)_2` and `(1001)_2`

Solution:

Solution is

Step-1 :
`=1_2+1_2`
`=1_10+1_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

Step-2 :
`=1+0_2+0_2`
`=1+0_10+0_10`
`=1_10`
`=1_2`
`:.` Sum`=1`

Step-3 :
`=0_2+0_2`
`=0_10+0_10`
`=0_10`
`=0_2`
`:.` Sum`=0`

Step-4 :
`=1_2+1_2`
`=1_10+1_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

Step-5 :
`=1+1_2+0_2`
`=1+1_10+0_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

3. Find addition of `(11110)_2` and `(1101)_2`

Solution:

Solution is

Step-1 :
`=0_2+1_2`
`=0_10+1_10`
`=1_10`
`=1_2`
`:.` Sum`=1`

Step-2 :
`=1_2+0_2`
`=1_10+0_10`
`=1_10`
`=1_2`
`:.` Sum`=1`

Step-3 :
`=1_2+1_2`
`=1_10+1_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

Step-4 :
`=1+1_2+1_2`
`=1+1_10+1_10`
`=3_10`
`=2xx1+1`
`=11_2`
`:.` Sum`=1` and carry`=1`

Step-5 :
`=1+1_2+0_2`
`=1+1_10+0_10`
`=2_10`
`=2xx1+0`
`=10_2`
`:.` Sum`=0` and carry`=1`

This material is intended as a summary. Use your textbook for detail explanation.
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