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Problem on Weighted and Un-weighted BCD

Example:

a) BCD (8 4 2 1)

b) 2 2 4 1

c) 3 3 2 1

d) Binary 

e) Excess 3

Solution:

i) 9’s complement of 8 = 1

ii) Representation of 1 in 2 2 4 1= 0001

iii) 1’s complement = 1110

i) 9’s complement of 6 = 3

ii) Representation of 3 in 2 2 4 1= 0101

iii) 1’s complement = 1010

We follow same procedure as above:

i) 9’s complement of 8 = 1

ii) Representation of 1 in 3 3 2 1= 0001

iii) 1’s complement = 1110

i) 9’s complement of 6 = 3

ii) Representation of 3 in 3 3 2 1= 0011

iii) 1’s complement = 1100

Q1. Which of the following is invalid 8 4 2 1 Code?

(i) 0010

(ii) 1100

(iii) 1001

(iv) 0111

Solution:

As we know 8421 is a weighted BCD code. 

So, Binary Coded Decimal (BCD) only represents 0 to 9 (0000 to 1001) and the rest of the digits 1010 to 1111(10 to 15) are invalid for BCD. 

[For more details about BCD please follow chapter: Binary Coded Decimal (BCD)]

So, 1100 means 12 is invalid for 8421 BCD. 

Option (ii) is correct.

Q2. Which of the following is an invalid Ex-3 code?

(i) 0011

(ii) 1100

(iii) 1101

(iv) 1001

Solution:

As we know Excess-3 is a non-weighted BCD code. 

So, Binary Coded Decimal (BCD) only represents 0 to 9 (0000 to 1001) and the rest of the digits 1010 to 1111(10 to 15) are invalid for BCD.

[For more details about BCD please follow chapter:  Binary Coded Decimal (BCD)]

So, 1101 means 13 in Excess-3.

Now after conversion from excess-3 to simple 8421 BCD.

13 – 3 = 10.

But 10 is invalid for BCD.

Option (iii) is correct.