Question
Wesign an adder for excess-3 decimal digits using a ROM. Add two
excess-3 digits and give the excess- 3 sum and a carry. For example,
with a carry of
inputs and outputs. What size ROM is required? Indicate how the truth table for the
ROM would be specified by giving some typical rows.
excess-3 digits and give the excess- 3 sum and a carry. For example,
with a carry of
inputs and outputs. What size ROM is required? Indicate how the truth table for the
ROM would be specified by giving some typical rows.
Ask by Davey Romero. in the United States
Dec 12,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
To design an adder for excess-3 decimal digits using a ROM, convert the excess-3 digits to decimal, add them, and convert the result back to excess-3. The ROM will have 100 entries for the 10 possible values of each digit, with inputs as 4-bit excess-3 digits and outputs as a 4-bit excess-3 sum and a 1-bit carry. The truth table specifies the output for each input combination.
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Beyond the Answer
When designing an adder for excess-3 decimal digits using a ROM, you’ll need to consider that excess-3 encoding represents decimal digits shifted by 3 in binary form. For the input pairs of digits, you’ll need a truth table that can represent each of the 16 possible combinations of the two excess-3 digits. The required ROM must accommodate these inputs, with a minimum size of 4 address lines for 16 combinations, which means a ROM size of
As for the truth table, for an input pair (A, B), you can have entries like:
| A (in excess-3) | B (in excess-3) | Sum (in excess-3) | Carry |
|---|---|---|---|
| 0011 (3) | 0100 (4) | 0111 (7) | 0 |
| 0101 (5) | 0011 (3) | 1000 (8) | 0 |
| 0110 (6) | 0111 (7) | 1001 (9) | 0 |
| 1000 (8) | 0101 (5) | 0001 (1) | 1 |
This gives a clear pathway for using the ROM to produce excess-3 output sums and carries based on the inputs.
For the block diagram, you would show the ROM connected to a multiplexer or similar circuit that takes the input pairs of excess-3 digits and processes them through the ROM to provide the desired outputs (sum and carry).
