Number system-2

Convert the number 672810 in to hexa-decimal number or 672810 = (     )16?

Sol:

672810 = 1A4816

Find the possible basses of the following numbers

a) \sqrt{45}=5            b) \frac{66}{6}=11

a) \sqrt{4 * b^{1} + 1 * b^{0}} = 5 * b^{0}

\sqrt{4b+1} = 5

4b=24

b=6

 Result is \sqrt{41}_{6} = 5_{6}

b)

\frac{6 * b^{1} +6 * b^{0}}{6 * b^{0}} = 1 * b^{1}+ 1 * b^{0}

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.

 

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