1.

Following are the numbers in various number systems. Two of the numbers are same. Identify them:1. (310)8 2. (1010010)2 3. (C8)16 4. (201)10OR Consider the following Boolean expression: (B’ + A)’ = B . A’ Identify the law behind the above expression and prove it using algebriac

Answer»

1. (310)8 = 3 * 82 + 1 * 81 + 0 * 80 

= 192 + 8 + 0 

= (200)10

2. (1010010)2 = 1 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20 

= 64 + 0 + 16 + 0 + 0 + 2 + 0 

= (82)10 

3. (C8)16 = C × 16 + 8 × 160

= 12 × 16 + 8 × 1 

= 192 + 8 

= (200)10 

Here (a) (310)8 and (C8)16 are same

OR 

This is De Morgan’s law (B’ + A’) = (B’)’ . A’ 

= B . A’

Hence it is proved



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