Page 31 - Math 7

Number Systems in Diff erent Bases

Convert 19 into binary system.

Power of base 2 2 6 2 4 2 3 2 2 2 1 2 °
Decimal Equivalent 32 16 8 4 2 1
Binary number 1 0 0 1 1
There is one 16 in 19. So There is no 4 in 3. So,
insert 1. insert 0.
Remainder = 19– 16 = 3 Remainder is again 3.
There is one 2 in 3. So
There is no 8 in 3. So, insert 1.
insert 0. Remainder =3 – 2 = 1.
Remainder is still 3.
There is one in 1. So
insert 1.
From the table, 19 = 1 × 16 + 0 × 8 + 0 × 4 + 1 × 2 + 1 × 1
= 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 + 1 × 2 °
3
4
1
2
= 10011
2
Convert 25 into binary system
Power of base 2 2 5 2 4 2 3 2 2 2 1 2 0
Decimal equivalent 32 16 8 4 2 1

Binary number 1 1 0 0 1

From the table, 25 = 1 u 16 + 1 u 8 + 0 u 4 + 0 u 2 + 1 u 1
= 1 u 2 + 1 u 2 + 0 u 2 + 0 u 2 + 1 u 2q = 11001
2
3
4
1
2
? 25 = 11001
2
Alternative method
We can convert a decimal number into binary system also by another method. In
this method, we should divide the given number successively by 2 until the quotient
is zero. The remainder obtained in each successive division is listed in a separate
column. For example:

2 19 Remainder
2 9 1
2 4 1
2 2 0 Arranging the remainders in reverse order:
2 1 0 10011 2
0 1

? 19 = 10011 2

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 29 Vedanta Excel in Mathematics - Book 7