Number System

Q.       What is bit?

Ans.: Bit: Computers represent information using bits. A bit has two possible values, namely, 0(zero) and 1(one).

Q.       What is byte?       

Ans.:  Byte: A bit strings of 8 bit (Either 0 or 1) is called 1 Byte.

Q.       Why the binary system is so important?  

Ans.: 0 and 1 only two number uses in binary numbering system. The base of binary number is two. Binary numbering system is super simple counting system. It’s possible to represent any types of number using 0 and 1. It’s very easy to simplify any electronic circuit and logic using two bit zero and one. So it’s more convenient to use binary number in electronic device. Computer accomplish of all types of internal work using binary numbering system.

Q.       Convert (123.45)₈ into (?)₁₆

Ans.: (123.45)₈ to binary = (001 010 011 . 100 101)₂

            (001 010 011 . 100 101)₂ = (0000 0101 0011 . 1001 0100)₂ = (53.94)₁₆

Q.       Convert (907.25)₁₆ to octal and decimal.

Ans.: (907.25)₁₆ = 1001 0000 0111 . 0010 0101 = 010 010 000 111. 001 001 010 = (2207.112)₈

            (907.25)₁₆ = 9 X 16² + 0 X 16¹ + 7 X 16⁰ + 2 X 16^-1 + 5 X 16^-2 = (2311.14453)₁₀

Q.       Convert (A9C.D4)₁₆ into (?)₁₀

Ans.: A X 2² + 9 X 2¹ + C X 2⁰ . D X 2^-1 + 4 X 2^-2 = 77.5 [Where A = 10, C = 12 and D = 13]

Q.       Define 2’s complement method.

Ans.: 2’s Complement method: If A is a binary number, then one’s complement of A is obtained by inverting each digit of A, and the two’s complement of A is its one’s complement plus 1.

Q.       Subtract (47)₁₀ from (87)₁₀ using 2’s complement method.

Ans.:  (87)₁₀ = (01010111)₂

            (47)₁₀ = (00101111)₂

            1’s complement of 47 is 11010000

            2’s complement of 47 is 11010001

            Now add 87 with 2’s complement of 47.

              01010111

  11010001

            100101000

Extra 1 bit is over flow so remove extra carry bit from 8 bit register. The answer is 00101000 means decimal 40.

Q.       Convert (58901)₁₀ to binary and octal.

Ans.: (58901)₁₀ =

2	58901
2	29450	1
2	14725	0
2	7362	1
2	3681	0
2	1840	1
2	920	0
2	460	0
2	230	0
2	115	0
2	57	1
2	28	1
2	14	0
2	7	0
2	3	1
2	1	1
2	0	1

            So the binary value: (1110011000010101)₂

            Octal value of (58901)₁₀ = 001 110 011 000 010 101 = (163025)₈