Addition in Other Bases

• I missed this part in the book. I assumed it was in chapter 3.
• I briefly covered this but let's do an official version.
• Remember how you add more than single digit integers in base 10

  
      2598
    + 8276
     -----
         
           start on the right and add 8+6
               The sum is 14
               Or a sum of 4 and a carry of 1
  
        1   <- so you write a 1 her
      2598  
    + 8276
     -----
         4  <- and the 4 here.
  
            You then have the complex problem of 1 + 9 + 7
                The sum is 17 
                Or a sum of 7 and a carry of 1.
       11
      2598
    + 8276
     -----
        74
        
               Repeating the process for 1 + 5 + 2
                   The sum is 8 and the carry is 0
      011
      2598
    + 8276
     -----
       874
               Next 0 + 2 + 8 = 10
  
     1011
      2598
    + 8276
     -----
      0874
  
               Since there was a last carry we need to add 1 + 0 + 0
     1011
      2598
    + 8276
     -----
     10874
      

• We do the same in other bases. But we need a different addition table.
  • Actually I lie, I just do it in base 10 and convert back.
  • But in binary you need 5 facts.

    +	0	1
    0	00	01
    1	01	10

  • and 1+1+1 = 11
• Add the following binary numbers

  • 
       011011110
       111110101
     -----------   
                     0+1 = 01
              0
       011011110
       111110101
     -----------   
               1
                   0+1+0 = 01
             00
       011011110
       111110101
     -----------   
              11
                   0+1+1 = 10
            100
       011011110
       111110101
     -----------   
             011
                  1+1+0 = 10
           1100
       011011110
       111110101
     -----------   
            0011
                  1+1+1 = 11
          11100
       011011110
       111110101
     -----------   
           10011
                  1+0+1 = 10
         111100
       011011110
       111110101
     -----------   
          010011
                  1+1+1 = 11
        1111100
       011011110
       111110101
     -----------   
         1010011
                  1+1+1 = 11
       11111100
       011011110
       111110101
     -----------   
        11010011
                  1+0+1 = 10
      111111100
       011011110
       111110101
     -----------   
       011010011
                  1+(0)+(0) = 01           
      111111100
       011011110
       111110101
     -----------   
      1011010011
            

• I don't care if you can do subtraction, multiplication or division in other bases.
  • If you do it frequently, you will learn how.
  • Otherwise
    • Use a calculator
    • Convert to base 10, do the math, convert back.