Question

Add 3.63ten x 104 to 6.87en x 103, assuming that you have only three significant digits, first with guard and round digits, and then without them.

Answer 1

3.63 * 10^4 + 6.87 * 10^3

First we must shift the smaller number to right to align the exponents.

With guard and round digits

This makes second operand equal to 0.687 * 10 ^4

Adding guard bit to first operand gives 3.630 * 10 ^4 + 0.687 * 10^4

Simplyfying gives 4.317 * 10^4 as we have three significant digits rounding off gives 4.32 * 10^4

Without guard and round digits

This makes second operand equal to 0.68 * 10 ^4

So 3.63 * 10^4 + 0.68 * 10^4

Gives 4.31 * 10 ^ 4 here we dont need to round off since there are only 3 significant bits