Discussion
The Boolean function
A(x, y, z) = Σ(0, 3, 4, 6)
B(x, y, z) = Σ(0, 1, 4, 7)
C(x, y, z) = Σ(1, 5)
D(x, y, z) = Σ(0, 1, 3, 5, 7)
can be implemented using a :
Answer: D
The functions can be implemented with an 8 × 4 ROM.
Each of the four functions depends on the same three variables x, y and z. Three address inputs select one of
\[ 2^{3} = 8 \ \text{words} \]
and each word must hold one output bit for each function, A, B, C and D, so the word length is 4 bits. The ROM size is therefore 8 words of 4 bits.
An 8 × 2 ROM has too few outputs. A 4 × 4 ROM has only two address lines, too few for three variables, and a 16 × 2 ROM has an unneeded fourth address line and still only two outputs.
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