Final answer:
When performing binary addition, we focus on adding individual bits of binary numbers from right to left, carrying over when necessary. Similarly, for whole numbers and fractions, we pay attention to proper alignment and place value during addition. Significant figures and rounding come into play for measurement accuracy in sums and differences.
Step-by-step explanation:
When performing binary addition, we are concerned with the individual bits (0s and 1s) of the numbers being added together. The basic principle to use in working with addition is to add each bit on the same column starting from the rightmost digit (the least significant bit) and going left. If the sum of the two bits is 2 (that is, 1+1), we write down a 0 and carry over a 1 to the next left column. If we sum 1+0 or 0+1, we write down a 1, and if it is 0+0, we write a 0, without carrying over.
Similarly, when working with whole numbers in base-10, we pay attention to the digits in each column, starting from the rightmost digit (the units) to the left (tens, hundreds, and so on). In whole numbers, carry over occurs when the sum of a column is greater than or equal to the base, which is 10 in this case. For instance, if we are adding 8+5, the sum is 13; we thus write down 3 and carry over 1 to the next column.
The process of rounding occurs when we deal with significant figures in addition and subtraction. The sum or difference must contain as many decimal places as the number with the least certain measurement. If we drop digits during this process, we use rounding rules: if the first dropped digit is 5 or greater, we round up; if it's less than 5, we round down.
Building intuition for addition and subtraction of fractions, consider the common denominators and the numerators, much like how we align digits in the same columns when adding whole numbers or bits in binary addition.