4 Convert the following a 3417 2 b B7E2416 6SolutionA FIR

4. Convert the following: a. (341)7 = ?2 ________________________ b. (B7E.24)16 = ?6

Solution

A) FIRST CONVERT TO DECIMAL => 3*7^2 +4*7^1+ 1*7^0 = (176)_10

now convert it to binary=> 176 divide by 2 leaves quotient =88 remainder=0

                                  => 88/2 leaves Q=44 R=0

                                      44/2 leaves Q=22 R=0

                                        22/2 leaves Q=11 R=0

                                        11/2 leaves Q= 5 R=1

                                        5/2 = Q= 2 R=1

                                         2/2= Q=1 R =0

                                         1/2 =Q=0 R=1

binary eq= 10110000

b) B7E.24 first convert to decimal => 11*16^2+7*16^1+14*16^0+2*16^-1+4*16^-2=2942.14

now divide integer part 2942 with 6 Q= 490 R=2

                                    490/6 Q=81 R=4

                                     81/6 Q=12 R=3

                                     12/6 Q=2 R=0

                                       2/6 Q=0 R=2

(20342)_6

now consider fraction part 0.14

0.14*6= 0.84 carry 0

0.84*6=5.04   carry =5

0.04*6=0.24 cary=0

0.24*6=1.44 carry=1

0.44*6=2.64 carry=2

0.64*6=3.84 carry=3

(0.050123)_6

(20342.050123)_6