ISRO CSE 2014 | Question: 27

Question

How many different $\text{BCD}$ numbers can be stored in $12$ switches ? (Assume two position or on-off switches).

• A. $2^{12}$
• B. $2^{12}-1$
• C. $10^{12}$
• D. $10^3$

Comments

is the answer d ?

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Edit : Title : ISRO 2014 SET A Question 27

Answer 1

1 Switch is equivalent to 1 bit  Cz  Switch store either on or off value like a bit can be 0 or 1.

So total 12 bits are there(cz there 12 switches)

Make 3 group of 12 bit . Means each group contain 4 bit.

(_ _ _ _) (_ _ _ _) (_ _ _ _)

      G1.        G2.       G3

Here in any group max 10 numbers can be stored Cz BCD numbers we have to store.

So 10*10*10 different BCD numbers can be stored in this 12 Switches. So Ans is option D) 10^3

Answer 2

With 4 bit we can represent 10 BCD no.

12 switches means 12 bit space.

Total 10*10*10 BCD no.

Comments

can you explain your solution. it is not clear to me. how it is 10*10*10.

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how please explain?

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Decimal Num	Binary Num	BCD Num
0	0000	0000
1	0001	0001
2	0010	0010
3	0011	0011
4	0100	0100
5	0101	0101
6	0110	0110
7	0111	0111
8	1000	1000
9	1001	1001
10	1010	0001 0000
11	1011	0001 0001
12	1100	0001 0010
13	1101	0001 0011
14	1110	0001 0100
15	1111	0001 0101

12 Switches --> 12 bits are divided into 3 groups

as each group contains 4 bits, hence we can store maximum 10 BCD numbers in that 4 bits i.e., from 0-9 

so probability of each group is 10 and total 3 groups=10*10*10

Hope this will clear your doubt.

Answer 3

BCD numbers = 4 bit.

Switch = 1 bit. (either on or off)

So, in 12 switches, we can store $\frac{12}{4}=3$ BCD numbers.

 

A BCD number ranges from 0 - 9. So 10 total values.

So, $10^3$

 

Option D

Answer 4

Answer : 10^3

Have a look at it : https://gateoverflow.in/13388/solve

Comments

12 switch means 12 bit means ??

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1 Switch is equivalent to 1 bit Cz Switch store either on or off value like a bit can be 0 or 1.