Morris Mano Edition 3 Exercise 5 Question 9 (Page No. 198)

Question

How many Unused Combinations are there in BCD adder?

Answer 1

A BCD ranges from 0000 to 1001 (0 to 9) in binary, therefore we need 4 bits to represent BCD.

That means we have a total of 2^4 or 16 combinations of 4 bits available, but we require only 10, i.e.

0000,0001,0010,0011,0100,0101,0110,0111,1000 and 1001

We are left with the remaining 6 or (16-10)  combinations i.e. 1010, 1011,1100, 1101,1110 and 1111

Now, a BCD adder takes 2 two BCD numbers {BCD1, BCD2)

So we have total 16 combinations for each, therefore total combinations we have can have for both BC1 and BCD2 = 16×16=256

Out of 16, only 10 were valid, so if for each 10 were valid inputs for BCD, for both BCD1 and BCD2 we have total 10×10 or 100 valid combination of bits

So invalid inputs that can be given are 256-100 i.e. 156