When turning in a homework problem, mark it with the exercise number shown in bold here. These will be the reference numbers I use in reporting back your standing on the homework.

**B.x1**: Design a PLA with four inputs and three outputs. The four inputs should be called`X`_{3},`X`_{2},`X`_{1}, and`X`_{0}, and the three outputs should be called`D`_{3},`D`_{4}, and`D`_{5}. The four inputs should be considered as forming a four-bit unsigned number,`X`_{3}`X`_{2}`X`_{1}`X`_{0}, with`X`_{3}as the most significant bit. Only the numbers 0 through 9 will ever be input; therefore, the outputs don't matter for any other input numbers. For input numbers 0 through 9, the outputs should be set as follows. The`D`_{3}output should be 1 if and only if the input number is divisible by three. The`D`_{4}output should be 1 if and only if the number is divisible by four. The`D`_{5}output should be 1 if and only if the number is divisible by five. Keep in mind that 0 is divisible by any non-zero integer. You should show your PLA design in the style of figure B.3.5 on page B-15. Your PLA should be minimal in the following sense:It should have as few vertical lines (product terms) as possible for any PLA that complies with the above specification.

It should have as few dots (AND or OR connections) as possible for any PLA that complies with the specification and the requirement of minimizing product terms.

Instructor: Max Hailperin