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, \( 1010+1001=0110 \) with a carry of \( 1(7+6=13) \). Draw a block diagram showing the required ROM inputs and outputs. What size ROM is required? Indicate how the truth table for the ROM would be specified by giving some typical rows.

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 \(2^4\) (16 entries). 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).