# What does "2 digit BCD number" mean?

When I read it, I think a $$\2\$$-digit BCD number is something between $$\0\$$ and $$\99\$$ in decimal. So, for example, $$\0100 1001\$$ is a $$\2\$$-digit BCD number and decimal equivalent of it is $$\49\$$ in my opinion.

However, this question confused me. I want to interpret $$\A_0\$$ or $$\A_1\$$ as a $$\4\$$ binary digits, representing a decimal number(BCD). And the circuit will add two $$\2\$$-digit binary numbers then. However, in such a scenario, I would expect to see an output labeling either as $$\S_0\$$ and $$\S_1\$$, which will also correspond to $$\4\$$ binary digits, but will represent BCD. Or, I would expect to see $$\S_0\$$ to $$\S_7\$$, each representing one binary digit.

In short, I am stuck in this question. Either I have some misunderstandings about wording, or I just don't get it.

I would appreciate if someone explains what this question wants to tell.

• A0, B0 and S0 are probably 4 bits wide Apr 2, 2020 at 0:47
• @jsotola hmm, so, I now think as follows, do you agree? if ADDITION : "S0, S1 and S2 will represent the addition result, S3 will output 0" if SUBT : <no idea> if COMPLEMENT : "S0 will be 9's complement of A0 and S1 will be 9's complemet of A1 and S2 will be 9's complement of B0 and S3 will be 9's complement of B1" Apr 2, 2020 at 0:52

One 2-digit BCD number is 8-bit wide and is made from

• High nibble = $$\A_1\$$ and

• Low nibble = $$\A_0\$$

Each nibble consists of 4 bits.
So e.g. $$\A_1 = 1000, A_0 = 0110\$$ gives $$\A = 86\$$ in BCD.

Similarly $$\B = B1 + B0\$$.

$$\S\$$ is $$\16\$$ bits
$$\= S_3 S_2 S_1 S_0\$$ $$\= 4 \times 4\$$-bit digits

So e.g. $$\S_4 S_3 S_2 S_1= 0001 \space 0010 \space 0100\space 1000 \$$,

Gives $$\S = 0001001001001000 = 1248\$$ in BCD.

The idea here is that you can treat a BCD digit as a single entity. Look at the components you have:

• Multiplexer (presumably for BCD digits)
• 9's complement unit

All of these use full BCD digits for their inputs and outputs, so you don't have to think about the individual bits. $$\C\$$ and $$\ADD\$$ are binary, but they never combine with the BCD signals -- they would only be used for the multiplexer selection signals.

• $$\C\$$, a binary signal
• $$\ADD\$$, a binary signal
• $$\A\$$, a two-digit BCD number with digits $$\A_0\$$ and $$\A_1\$$
• $$\B\$$, a two-digit BCD number with digits $$\B_0\$$ and $$\B_1\$$

And the outputs are:

• $$\S\$$, a collection of four BCD digits, which could be either:
• A single number that represents the sum or difference of the inputs, with digits $$\S_0\$$ through $$\S_4\$$.
• Two numbers which represent the complements of the two inputs, with $$\S_1S_0 = \mathrm{complement}(A_1A_0)\$$ and $$\S_3S_2 = \mathrm{complement}(B_1B_0)\$$.

The instructor wants a $$\4\$$ digit output from two $$\2\$$-digit inputs. Each digit, of course, is $$\4\$$ bits.

It's not entirely clear, but it looks to me like he or she expects the outputs $$\S_3..S_0\$$ to output the $$\9\$$'s complement of $$\B_1 B_0 A_1 A_0\$$ when $$\C = 1\$$ So if the two numbers are $$\A = 02\$$ and $$\B = 12\$$ then $$\S = 8797\$$ when $$\C = 1\$$.

For addition you'd expect $$\S_3\$$ to remain $$\0\$$, and $$\S_2\$$ to be $$\0\$$ or $$\1\$$.

If $$\A = 10\$$ and $$\B = 1\$$ then it should be $$\0009\$$.

If $$\A = 1\$$ and $$\B = 10\$$ then I think it should be $$\9991\$$.

• well, thanks for the answer. Everything makes sense, except the A=1 and B=10 part, subtraction is not clear in my head also. While saying 9991, are you taking 9's compliment with 4 digits? Can you ellaborate a little bit ? Apr 2, 2020 at 2:00
• Yes, extending the 2 digit number with two leading zeros before taking the complement. Apr 2, 2020 at 2:01
• For subtracting, I am planning to just take 9's comp. of each BCD digit, and then add A0 + complement of B0 direct sum to S0 and Cout1 to second BCD adder, and add A1 + comp of B1 there. Then, direct sum to S1 and Cout2 to S2 while leaving S3 as logic 0. Do you think it would work? Apr 2, 2020 at 2:05
• well, it turned out that your 9991 was correct, it is sad that I did not get it that time(it was 6:00 am in my time zone) and did it as 9091 instead of 9991. Apr 2, 2020 at 11:19