Question

1011+111 in binary form

Answer 1

10010

Explanation:

`1011=1(2)^3+0(2)^2+1(2)^1+1(2)^0`

`111=1(2)^2+1(2)^1+1(2)^0`

So
`1011+111` gives us:

`1(2)^3+0(2)^2+1(2)^1+1(2)^0`

`+`

`1(2)^2+1(2)^1+1(2)^0`

-----------------------------------------------------

Combine like terms:

`1(2)^3+(0+1)(2)^2+(1+1)(2)^1+(1+1)(2)^0`

`1(2)^3+1(2)^2+(2)(2)^1+(2)(2)^0`

We aren't allowed to have a coefficient bigger than 1.

I'm going to replace
`2^0` with 1 and
`2` with
`(2)^1`:

`1(2)^3+1(2)^2+(2)^2+(2)^1(1)`

I want a
`2^0` number:

`1(2)^3+1(2)^2+1(2)^2+1(2)^1+0(2)^0`

Combine like terms:

`1(2)^3+2(2)^2+1(2)^1+0(2)^0`

`2(2)^2=2^3`:

`1(2)^3+2^3+1(2)^1+0(2)^0`

Combine like terms:

`2(2)^3+1(2)^1+0(2)^0`

We can rewrite the first term by law of exponents:

`2^4+1(2)^1+0(2)^0`

`1(2)^4+1(2)^1+0(2)^0`

So the binary form is:

`10010`

Maybe you like this way more:

Keep in mind 1+1=10 and that 1+1+1=11:

Setup:

1 0 1 1

+ 1 1 1

------------------------------

(1) (1) (1)

1 0 1 1

+ 1 1 1

------------------------------

1 0 0 1 0

I had to do some carry over with my 1+1=10 and 1+1+1=11.