Respuesta :
Answer:
10010
Step-by-step explanation:
[tex]1011=1(2)^3+0(2)^2+1(2)^1+1(2)^0[/tex]
[tex]111=1(2)^2+1(2)^1+1(2)^0[/tex]
So [tex]1011+111[/tex] gives us:
[tex]1(2)^3+0(2)^2+1(2)^1+1(2)^0[/tex]
[tex]+[/tex]
[tex]1(2)^2+1(2)^1+1(2)^0[/tex]
-----------------------------------------------------
Combine like terms:
[tex]1(2)^3+(0+1)(2)^2+(1+1)(2)^1+(1+1)(2)^0[/tex]
[tex]1(2)^3+1(2)^2+(2)(2)^1+(2)(2)^0[/tex]
We aren't allowed to have a coefficient bigger than 1.
I'm going to replace [tex]2^0[/tex] with 1 and [tex]2[/tex] with [tex](2)^1[/tex]:
[tex]1(2)^3+1(2)^2+(2)^2+(2)^1(1)[/tex]
I want a [tex]2^0[/tex] number:
[tex]1(2)^3+1(2)^2+1(2)^2+1(2)^1+0(2)^0[/tex]
Combine like terms:
[tex]1(2)^3+2(2)^2+1(2)^1+0(2)^0[/tex]
[tex]2(2)^2=2^3[/tex]:
[tex]1(2)^3+2^3+1(2)^1+0(2)^0[/tex]
Combine like terms:
[tex]2(2)^3+1(2)^1+0(2)^0[/tex]
We can rewrite the first term by law of exponents:
[tex]2^4+1(2)^1+0(2)^0[/tex]
[tex]1(2)^4+1(2)^1+0(2)^0[/tex]
So the binary form is:
[tex]10010[/tex]
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.
