Question

Add (10111)2and (11010)2by working through each

step of the algorithm for addition given in the text.

Short answer

110001

Step-by-step solution

Step 1:

Note that n = 5. Initially the carry is c = 0 , and we start the for loop with j = 0. Since $a_0=1$and $b_0=0$, we set d to be floor of $(1-0-0)/2=0$then $s_o=1+0+0-2-0$which equals 1 ,and finally c = 0. At the end of the first pass , then , the right - most digit of the answer has been determined ( it's a 1 ) , and there is a carry of 0 into the next column .

Now j = 1 and we computed to be floor of $\left(a_1+b_{1}c\right)/2=$floor of $(1+1+0)/2$

whereupon $s_1$becomes $1+1+0-2-1=0$ and c is set to 1. Thus far we have determined that the last two bits of the answer are 01 ( from left to right ) , and there is a carry of 1 into the next column .

The next three passes through the loop are similar . As a result of the pass when j = 2 we set d = 1 , $s_2$= 0 and then c = 1 .When c = 1, we obtain $d=1,s_4=1$and then c = 1 . Finally , when j = 4, we obtain $c=1$and then $s_5=1$. At this point the loop is terminated , and when we execute the final step , 11 0001. Thus the answer is.