Question

What is the best capacity of the ROM for the realization of an adder for adding 3 numbers (A, B, C) simultaneously, all of the inputs are 3-bit binary numbers

Answer 1

The best capacity of a ROM to realize an adder for adding three 3-bit binary numbers is 2560 bits, which would most likely require using a standard 4Kb ROM due to the standardized sizes of ROMs.

Step-by-step explanation:

To determine the best capacity of the Read-Only Memory (ROM) for realizing an adder that adds three 3-bit binary numbers (A, B, C) simultaneously, we need to calculate the total number of possible input combinations and the corresponding amount of storage required to hold the precomputed sum for each combination. With three 3-bit numbers, there are 23 = 8 possible values for each number. Since there are three such numbers, the total number of combinations is 83 or 512 possible input states. Each input state will produce a sum which could be as large as 3 x 23 - 1 = 21, which is a 5-bit number (including the potential carry bit).

Each of the 512 combinations needs to store its corresponding 5-bit result. Thus, the total capacity required for the ROM is 512 combinations times 5 bits, resulting in a 2560-bit ROM. However, ROM sizes are usually standardized, and you might have to use the closest standard size, which would likely be a 4Kb ROM for this purpose.

Answer 2

The best capacity of the ROM for adding 3 numbers simultaneously is 512.

Step-by-step explanation:

The best capacity of the ROM for the realization of an adder for adding 3 numbers simultaneously can be determined by calculating the number of input combinations possible. In this case, we have three 3-bit binary numbers (A, B, C). Each binary number has 23 = 8 possible combinations since 3 bits can represent numbers from 0 to 7. Since we have three input numbers, the total number of combinations is 8 x 8 x 8 = 512.

To accommodate 512 input combinations, we will need a ROM with a capacity of at least 512, which means it should have at least 512 addressable locations or cells. Therefore, the best capacity of the ROM for this adder is 512.