1+1 = 10, 1+2 = 3

JavaScript ES6, 87 97¹ 100² 106³ 102 101 98 100⁴ 93 88 86 bytes

e=>eval(e.match`[2-9]`?e:`(${e.replace(/[\d.]+/g,"('0b'+$&e14)/16384")}).toString(2)`)

Demo + explanation:

function c(e){
    return eval(                        
      e.match`[2-9]`?                  //check if there are numbers 2 to 9
        e:                             //if there're, just compute the result
        "("+                           
         e.replace(                    //otherwise replace...
           /[\d.]+/g,                  //any number...
           "(('0b'+$&e14)/16384)"    //...with itself converted to base 10
         )
        +").toString(2)"               //compute the result and convert it to binary
    )
}

document.write(
   c("1.1*1.1")+"<br>"+
   c("1010+10-1")+"<br>"+
   c("102+10-1")+"<br>"+
   c("1+2+3")+"<br>"+
   c("10*10*10")+"<br>"+
   c("11*11*11")+"<br>"+
   c("10*11*12+1")+"<br>"+
   c("10.1*10.1")+"<br>"+
   c("20.2*20.2")+"<br>"+
   c("10/5")+"<br>"+
   c(`10
      +
      10
      -
      1`)
)

^{1 - forgot about floats
2 - again floats problem: parseInt floors binary so I have to multiply by 1e14 and then divide by 16384
3 - hope that's achieved the given task, now start to golf :D
4 - there was a bug with dividing}

Japt, 77 72 62 60 62^* 60 59 51 bytes

OvUf"[2-9]" ?U:"({Ur"[\\d.]+""º$&e14+P n2 /2pE¹"})¤

Explanation (more or less the same as for the JS answer):

Ov                       //eval...
  Uf"[2-9]"              //if input contains the digits 2 to 9
    U:                   //then it's base 10, just compute
    Ur"[\\d.]+"          //otherwise replace all the numbers
    "º$&e14+P n2 /2pE¹"  //with their base 10 equivalents
                         //I.e., take every number, multiple by 10^14, convert to
                         //base 10 and divide by 2^14
                         // º and ¹ are multiple brackets
    ¤                    //means "s2", i.e. convert the result to binary
                 

Try it online!

^{* didn't divide properly}

Jolf, 31 bytes, noncompeting

I added a decent amount of functions inspired by this challenge, and, as thus, it is considered noncompeting. I'm happy because I finally implemented unary functions (like (H,S,n)=>val in ES6, but are supported in ES5!)

? hi"[2-9]"~eiB~epT mpvid|m'H2H
? hi"[2-9]"                     if the input contains any of 2..9
           ~ei                   evaluate i (implicitly print)
                                else
                   _mpvid        map the input split into number groups
                          m'H2    to H as a binary float
                         |    H   (or keep H, if that doesn't work)
                 pT              join by spaces
               ~e                evaluate
              B                  convert to binary (implicitly print)

Test suite, Try your own input, or manually set the input.