**Convert the number 6728**_{10} in to hexa-decimal number or 6728_{10 }= ( )_{16}?

_{10}in to hexa-decimal number or 6728

_{10 }= ( )

_{16}?

Sol:

6728_{10} = 1A48_{16}

**Find the possible basses of the following numbers**

a) b)

a)

Result is :

b)

6b+6 = 6b+6

The above equation satisfies for any value of b mathematically. But as per the number base rule the base value should not be less than the first value i.e. 6 in the above equation.

So the above equation satisfies for any base which is >6 for example 7.

#### In a positioned weighted system if P & Q are the successive bits in the equations PQ=25 and QP=31. find out P and Q?

sol:

First it is indicated that the Q and P are successive digits i.e.

Q=P+1.

Pb + Q = 25 –1

Qb + P =31 — 2

Substituting the Q value in equation -2 then

(P+1)b +P = 31

Pb+b+P = 31 — 3

By subtracting equation 1 from equation 3 then

b-1 =6

b=7.

by substituting b value in equation 3

8P = 24

P=3

Q=P+1=3+1=4.

Quarter Column