**Que 1: Prove that A+A'B = B+B'A = A+B.**

`Ans 1: A+A'B = (AB' + AB) + A'B = AB' + (AB + A'B) = AB' + B`

`A+A'B = (AB' + AB) + A'B`

= AB' + AB + AB + A'B

= (AB' + AB ) + (AB + A'B)

= A + B

= AB' + AB + AB + A'B

= (AB' + AB ) + (AB + A'B)

= A + B

`Que 2: Convert 25.625 fraction decimal numbers into binary number system.`

` Ans 2: The weights in binary numbers are 2^{5}(32), 2^{4}(16), 2^{3}(8), 2^{2}(4), 2^{1}(2), 2^{0}(1), 2^{-1}(.5), 2^{-2}(.25), 2^{-3}(.125) and so on.`be mentioned

25.625 can be written as 16+8+1+0.5+0.125, If the weight value exists it will

`as 1 else 0. So, 25.625 can be written as`

**11001.101**.`Que 3: Convert 1011001 in 2’s complement and 1’s complement.`

**Ans 3: **To convert binary numbers into 2’s complement, bits of binary numbers are inverted. So, 1011001 can be represented as 0100110 in 2’s complement.

To convert binary numbers into 1’s complement, Bits of the binary numbers are inverted except the last 1 in the binary number. So, 1011001 can be represented as **0100111** in 1’s complement.

`Que 4: What is gray code representation and how to convert from binary number to gray code?`

**Ans 4:** Gray code, is an ordering of the binary numeral system such that two successive values differ in only one bit. eg. 00, 01, 11, 10.

This representation can be used to reduce the combinational logic.

Refer the Fig. 1 for Gray code to binary code converter.

`Que 5: Convert 10/3 into Base 3 system.`

**Ans 5:** In base 3 system, weights of the number are 3^{4}(81), 3^{3}(27), 3^{2}(9), 3^{1}(3), 3^{0}(1), 3^{-1 }(1/3), 3^{-2}(1/9) and so on.

10/3 can be written as 9/3 +1/3 = 3 + 1/3, So the Base 3 representation of 10/3 would be **10.1.**

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