The amount of ROM needed to implement a 4-bit multiplier is:

Concept

A ROM implements a combinational function by using the input bits as address lines and storing one output word at every address.

For n address bits and m output bits, the required capacity is 2n words × m bits per word.

Application

1. The multiplier has two 4-bit operands, so the ROM address receives n = 4 + 4 = 8 input bits.

2. Eight address bits select 28 = 256 input combinations.

3. The largest unsigned product is 15 × 15 = 225. Since 225 is 11100001 in binary, each stored product needs m = 8 bits.

4. Therefore, the ROM capacity is 256 words × 8 bits per word = 2048 bits = 2 Kbits.

Cross-check

Each 4-bit operand has 16 possible values, so the input table contains 16 × 16 = 256 rows. Storing one 8-bit product in each row again gives 256 × 8 = 2048 bits.

Result: The required ROM capacity is 2 Kbits.