Use the Egyptian algorithm to multiply.
34 × 134

Question

Quizplus · Accepted Answer

Using the Egyptian algorithm, we have:
34 × 134
= 34 × (2 × 67)
= 34 × (2 × (64 + 3))
= 34 × (2 × 64 + 2 × 3)
= 34 × (128 + 6)
= 34 × 128 + 34 × 6
= 4352 + 204
= 4556
Converting to hexadecimal gives us 11ebb939_4a4d_81c7_9e6c_c7de3902ff78_TB8446_11. 34 = 100010 (in binary)
134 = 10000110 (in binary)
According to the Egyptian algorithm:
1) Write 34 and 134, with a single space between them.
100010   10000110 
2) Halve the first number repeatedly until you get to 1, writing the results underneath:
100010   10000110 
  50005    
  25002    
  12501 
   6250    
   3125    
   1562    
    781   
    390   
    195    
     97    
     48  
      24   
      12  
       6   
       3   
       1   
3) Cross out all rows where the number on the left is even. Write the remaining numbers on the right (in binary) next to the corresponding number on the left:
100010   10000110 
  50005       0 
  25002    10000110 
  12501       0 
   6250    10000110 
   3125    10000110 
   1562    10000110 
    781    10000110 
    390    10000110 
    195    10000110 
     97    10000110 
     48     1100010 
      24    11000000 
      12    11000000 
       6    10110000 
       3    10001010 
       1    10001010 
4) Add up all the numbers on the right that are not crossed out to get the answer: 
10000110
+10000110
+10000110
+10000110
+10000110
+10000110
+10000110
+1100010
= 110111110

Converting the answer back to decimal gives us 4468.
Therefore, the best choice is (B) 11ebb939_4a4d_81c7_9e6c_c7de3902ff78_TB8446_11.

Use the Egyptian Algorithm to Multiply