decimal equivalent of BCD

Question

What is decimal equivalent of BCD 11011.1100 ?

(A) 22.0   (B) 22.2  (C) 20.2   (D) 21.2

Comments

is 11011 is a BCD no.?

Answer 1

BCD is a weighted Code which is 8421.
and BCD Code 0-9 digits only.
for eg. let's take N=12, and now convert 12 into binary which is (1100)2
now Convert N=12 into BCD(Binary Coded Decimal) which is 0001 0010

How do we convert the Binary number to BCD: just ADD 0110 into the Binary Number.

So 1100+0110=10010   (make pair of 4 from right So 0001 0010 which is 12)

Now Move to the question:-
given BCD is 11011.1100 make pair of 4 we see its range is not between 0-9..So we need to correction it by adding 0110 to the place where the range is not between 0-9.

0001 1011.1100
+
0000 0110.0110
=
0010 0010.0010
now make pair of 4 and we see
22.2
So ans is B

Comments

Sir, It means given code is not in BCD, for ex 22.2 in BCD is 00100010.0010, and in question it is given as 11011.1100. If we  want to convert decimal to binary this code we cant obtain. I didnt get that adding 6 concept clearly, i mean why do we need to add?

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"If we  want to convert decimal to binary this code we cant obtain."
Directly not....but indirectly possible..
take Eg. lets N=13 and BCD Representation is 0001 0011 
now subtract 6 in BCD (0110)₂
So 0001 0011
-
              0110
=
              1101
S0 binary representation of  N=13 is (1101)₂
 

" I didnt get that adding 6 concept clearly, i mean why do we need to add?"
the reason behind adding 6 is that there are 2⁴=16 (0-15) possible value for 4bit BCD. but only 10 (0-9) value is valid. So adding 6 we convert invalid value to valid value 

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I think question should be a "decimal equivalent of BCD of given binary no" Otherwise it do not make sense.

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option B is correct.

Answer 2

BCD Addition Summary