Q.Do the following conversions from decimal number to other number systems.

Use repeated division by the target base; the remainders read bottom-to-top give the answer.

(i)   (54)10  : 54/2=27 r0; 27/2=13 r1; 13/2=6 r1; 6/2=3 r0; 3/2=1 r1; 1/2=0 r1
              -> (110110)2
(ii)  (120)10 : 120/2=60 r0; 60/2=30 r0; 30/2=15 r0; 15/2=7 r1; 7/2=3 r1; 3/2=1 r1; 1/2=0 r1
              -> (1111000)2
(iii) (76)10  : 76/8=9 r4; 9/8=1 r1; 1/8=0 r1              -> (114)8
(iv)  (889)10 : 889/8=111 r1; 111/8=13 r7; 13/8=1 r5; 1/8=0 r1 -> (1571)8 …

The idea. To convert a decimal integer into base r, use the repeated-division method: divide by r, note the remainder, divide the quotient again, and repeat until the quotient is 0. The remainders, read from last to first (bottom-to-top), are the digits of the answer — because each division peels off the next place-value digit.

(i) (54)10 to binary — divide by 2:

Reading up: (110110)2. Check: 32+16+4+2 = 54.

(ii) (120)10 to binary:

Reading up: (1111000)2. Check: 64+32+16+8 = 120.

(iii) (76)10 to octal — divide by 8:

76 / 8 = 9  remainder 4
 9 / 8 = 1  remainder 1
 1 / 8 = 0  remainder 1
Reading up: (114)8        Check: 1x64 + 1x8 + 4 = 76

(iv) (889)10 to octal:

889 / 8 = 111 remainder 1
111 / 8 = 13  remainder 7
 13 / 8 = 1   remainder 5
  1 / 8 = 0   remainder 1
Reading up: (1571)8       Check: 512 + 5x64 + 7x8 + 1 = 889

(v) (789)10 to hexadecimal — divide by 16:

789 / 16 = 49 remainder 5
 49 / 16 = 3  remainder 1
  3 / 16 = 0  remainder 3
Reading up: (315)16       Check: 3x256 + 1x16 + 5 = 789
``` …