BCD = Binary Coded Decimal
ie Decimal numbers, numbers in the range 1 to 9 converted into a binary form.
Look at the table below:
Code:
Binary(4bits) Decimal Hexadecimal BCD
0000 0 0 0
0001 1 1 1
0010 2 2 2
0011 3 3 3
0100 4 4 4
0101 5 5 5
0110 6 6 6
0111 7 7 7
1000 8 8 8
1001 9 9 9
1010 10 A Not Valid
1011 11 B Not Valid
1100 12 C Not Valid
1101 13 D Not Valid
1110 14 E Not Valid
1111 15 F Not Valid
Using 4 bits we can count up to 15, in BCD we can only count up to 9, numbers 10 to 15 should not, cannot, must not, exist as a BCD digit.
Consider the decimal number 2793, to convert this to BCD, just look at each digit
2 = 0010
7 = 0111
9 = 1001
3 = 0011
So, 2793 is 0011 0111 1001 0011 in BCD.
If you have a binary number 1110, this is an invalid BCD number and has the decimal value 14,
so the BCD equivalent would be 14 = 0001 0100
1 = 0001
4 = 0100
Let me just emphasise 1110
is not a valid BCD number, but it is a binary number so just convert the binary number to a decimal number and then you can convert decimal to BCD by a simple inspection process.
As far as adding "6" goes, to me that feels like a bit of a confuser, but is does work.
Code:
1110 +
0110
------
1 0100
Your text book also write some BCD numbers as 1001000001000011 or some such nonsense.
Again I think this is just plain confusing.
BCD is groups of four bits each representing a decimal digit, so why dont they write it as
1001 0000 0100 0011 ???
But then when did anything in a school textbook have to be logical?
Just my distorted opinion.
As a side issue, BCD is usually in 1248 form, but there are others such as 1245 BCD and Grey Code, and others.
Grey Code is quite common, but I cannot remember seeing 1245 used, but then that is just me.
Does this help?
JimB