Based on the paragraph given below answer the following question: The traditional methods of combinational circuits involve simplification and realization using gates. Using these methods, complex functions have been integrated and are easily available in IC form. There is an attractive array of devices like a multiplexer, demultiplexer, decoders, comparators, parity generators/checkers, which significantly reduce IC package count thereby reducing the system cost. The system design is greatly simplified because the laborious and time-consuming simplification methods are generally not required with these devices. This also improves the reliability of the system by reducing the number of external wired connections. But they have some limitations as well. Different memories like ROM, PROM can also be used to implement combinational circuits without much simplification. In a BCD Subtractor if the sum of minuend and the nine’s complement of the subtrahend is not a valid BCD Code, then which binary number is added to the sum to get the correct answer?
Based on the paragraph given below answer the following question: The traditional methods of combinational circuits involve simplification and realization using gates. Using these methods, complex functions have been integrated and are easily available in IC form. There is an attractive array of devices like a multiplexer, demultiplexer, decoders, comparators, parity generators/checkers, which significantly reduce IC package count thereby reducing the system cost. The system design is greatly simplified because the laborious and time-consuming simplification methods are generally not required with these devices. This also improves the reliability of the system by reducing the number of external wired connections. But they have some limitations as well. Different memories like ROM, PROM can also be used to implement combinational circuits without much simplification. In a BCD Subtractor if the sum of minuend and the nine’s complement of the subtrahend is not a valid BCD Code, then which binary number is added to the sum to get the correct answer? Correct Answer 0110
Binary Coded Decimal (BCD) code:
- BCD is a way to express each of the decimal digits with a binary code.
- In this code, each decimal digit is represented by its 4-bit binary equivalent.
- Also, with four bits we can represent sixteen numbers (0000 to 1111)
- But as there are 10 decimal digits from 0 to 9, BCD code uses only the first ten of these (0000 to 1001). The remaining six code combinations i.e. 1010 to 1111 are invalid in BCD.
|
Decimal Number |
Binary Number |
Binary Coded Decimal (BCD) |
|
0 |
0000 |
0000 |
|
1 |
0001 |
0001 |
|
2 |
0010 |
0010 |
|
3 |
0011 |
0011 |
|
4 |
0100 |
0100 |
|
5 |
0101 |
0101 |
|
6 |
0110 |
0110 |
|
7 |
0111 |
0111 |
|
8 |
1000 |
1000 |
|
9 |
1001 |
1001 |
|
10 |
1010 |
0001 0000 |
|
11 |
1011 |
0001 0001 |
|
12 |
1100 |
0001 0010 |
|
13 |
1101 |
0001 0011 |
|
14 |
1110 |
0001 0100 |
|
15 |
1111 |
0001 0101 |
BCD subtraction using 9’s complement method:
- At first, the decimal equivalent of the given Binary Coded Decimal (BCD) codes is found out.
- Then the 9’s complement of the subtrahend is done and then that result is added to the number from which the subtraction is to be done.
- If there is any carry bit then the carry bit may be added to the result of the subtraction.
Special case:
- If the sum of minuend and the nine’s complement of the subtrahend is not a valid BCD Code, i.e., when any BCD digit greater than 1001 occurs, 6 is added to generate a carry bit and cause the sum to become a valid entry.
- The reason for adding 6 is that there are 16 possible 4-bit BCD values (since 24 = 16), but only 10 values are valid (0000 through 1001). So by adding a six to the invalid code, we can get a valid code.
Example:
Let 0101 is added with 0110
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(0101)2 → (5)10 and (0110)2 → (6)10
(5)10 + (6)10 = (11)10