Finish Chpapter 2

• Conversions from other bases to base 10
  • Use the same techniques
  • Ethier express as a polynomial.
  • Or use Horner's method.
  • Example: Convert from $F2C3_16$ to decimal

       polynomial
       $F2C3_16 = 15\times16^3 + 2 \times 16^2 + 12 \times 16^1 + 3 \times 16^0$
       $15 \times 4096 + 2 \times 256 + 12 \times 16 + 3$
       $61440 + 512 + 192 + 3$
       62,147
    
       horners:
       F     0 * 16 + 15 =    15
       2    15 * 16 +  2 =   242
       C   242 * 16 + 12 =  3884
       3  3884 * 16 +  3 = 62147
            

• Coversions from base 10 to other bases:
  • Use the same method (continue to divide by the base)
  • Convert 62147 to octal

                     7768 R 3
                   ------
                  8|62147      or       on a calculator 
                    56                   62147 / 8 = 7768.375
                     61                        .375 x 8 = 3      so 3
                     56
                      54
                      48
                       67
                       64
                       --
                        3
    
                       971 R 0
                    ------
                  8 | 7768
                      72
                       56
                       56
                         8
                         8
                        -- 
                         0
    
                     121 R 3
                   -----
                  8| 971
                     8
                     17
                     16 
                      11
                       8 
                      --
                       3
    
                      15   R 1
                    -----
                   8|121
                      8
                      41 
                      40
                      --
                       1
    
                       1 R 7
                     ---
                    8|15
                       8
                       - 
                       7
    
                       $171303_8$
    
             

• Conversions between multiple bases:
  • If it is between binary, hex and octal, I change to binary and then to whatever I need.
  • Example: Convert $171303_8$ to hex.
    1 7 1 3 0 3 001 111 001 011 000 011 001111001011000011 00 1111 0010 1100 0011 F 2 C 3 $F2C3_{16}$
  • If it is between any other bases change to base 10 then whatever I need.
  • I will no ask you to do this.
• I will ask you to convert between base 10 and base 2 both ways
• I will ask you to convert between base 2 and Hex and Octal, all ways.
• In the end everything is represented in binary inside a computer.
• We call 8 binary digits a byte