addition_style.css

/*some sexy styling*/

* {
    margin: 0;
    padding: 0;
    font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Open Sans', 'Helvetica Neue', sans-serif;
    font-size: 16px;
}

.info {
    padding: 20px;
}

h2 {
    margin-bottom: 2rem;
    font-size: 2rem;
}

.base {
    margin: 1rem 20px;
    padding: 10px;
    border: 1px solid grey;
}

.result::before {
    border-left: 1px solid black;
    padding: 2px 5px;
    margin-left: 12px;
}

input[type="checkbox"] {
    margin: 0 4px;
}

input:disabled {
    opacity: 0;
}


/*====================================================actual logic===============================*/
/*setting result to 0 by default, so we only have to check when to set it to 1*/
.result::before {
    content: "0";
}

/*setting the non-carried child module as the default one*/
.carried {
    display: none;
}

/*in case we need to carry a bit, display the carried*/
/*when we're in any module and both bits are checked*/
.module > input:nth-child(1):checked ~ input:nth-child(2):checked ~ .carried,
/*when we're in a carried module and at least one bit is checked*/
.carried > input:nth-child(1):checked ~ .carried,
.carried > input:nth-child(2):checked ~ .carried {
    display: block;
}

/*when we're in any module and both bits are checked*/
.module > input:nth-child(1):checked ~ input:nth-child(2):checked ~ .non-carried,
/*when we're in a carried module and at least one bit is checked*/
.carried > input:nth-child(1):checked ~ .non-carried,
.carried > input:nth-child(2):checked ~ .non-carried {
    display: none;
}

/*calculating base module first*/
.base > input:nth-child(1):checked ~ input:nth-child(2):not(:checked) ~ .result::before,
.base > input:nth-child(1):not(:checked) ~ input:nth-child(2):checked ~ .result::before 
{
    content: "1";
}

/*calculating for child modules*/
/*.non-carried: result will only be 1 if only one bit is set*/
.non-carried > input:nth-child(1):not(:checked) ~ input:nth-child(2):checked ~ .result::before, /*only second bit checked*/
.non-carried > input:nth-child(1):checked ~ input:nth-child(2):not(:checked) ~ .result::before /*only first bit checked*/
{
    content: "1";
}

/*carried: result will be one if none of the bits is set or both*/
.carried > input:nth-child(1):not(:checked) ~ input:nth-child(2):not(:checked) ~ .result::before, /*none checked*/
.carried > input:nth-child(1):checked ~ input:nth-child(2):checked ~ .result::before /*both checked*/ {
    content: "1";
}