The binary number system is a number system that uses only two digits: 0 and 1. It is also called the base-2 number system.
Example 1: Convert the Decimal Number (98)10 into Binary.
Solution:Ā
Thus, Binary Number for (98)10 is equal to (1100010)2
Example 2: Convert the Binary Number (1010101)2 to a decimal Number.
Solution:Ā
Given Binary Number, (1010101)2
= (1 Ć 20) + (0 Ć 21) + (1 Ć 22) + (0 Ć 23) + (1 Ć 24) + (0 Ć 25) + (1 Ć26)
= 1 + 0 + 4 + 0 + 16 + 0 + 64
= (85)10Thus, Binary Number (1010101)2 is equal to (85)10 in decimal system.
Example 3: Divide (11110)2 by (101)2.
Solution:
Example 4: Add (11011)2 and (10100)2.
Solution:
Hence, (11011)2 + (10100)2 = Ā (101111)2
Example 5: Subtract (11010)2 and (10110)2.
Solution:Ā
Hence, (11010)2 - (10110)2 = (00100)2
Example 6: Multiply (1110)2 and (1001)2.
Solution:Ā
Thus, (1110)2 Ć (1001)2 = (1111110)2
Example 7: Convert (28)10 into a binary number.
Solution:
Hence, (28)10 is expressed as (11100)2.
Example 8: Convert (10011)2 to a decimal number.
Solution:
The given binary number is (10011)2.
(10011)2 = (1 Ć 24) + (0 Ć 23) + (0 Ć 22) + (1 Ć 21) + (1 Ć 20)
= 16 + 0 + 0 + 2 + 1 = (19)10
Hence, the binary number (10011)2 is expressed as (19)10.
Practice Problems
Question 1. Convert the decimal number (98)āā into binary.
Question 2. Divide the binary number (11110)ā by (101)ā
Question 3. Find the 2's complement of the binary number (1011)ā.
Question 4. Multiply the binary numbers (1110)ā and (1001)ā.
Question 5. Subtract the binary numbers (11010)ā and (10110)ā.
Question 6. Add the binary numbers (11011)ā and (10100)ā.
Answer:-
1. (1100010)2ā, 2. (110)2ā, 3. (0101)2, 4. (1111110)2, 5. (00100)2āā, 6. (101111)2
