
COSC 2P12 Last Modified: Sunday, 22Oct2017 16:45:28 EDT 
2017 
3.6
3.18
3.24
Manipulate the following Boolean expression in such a way so that it can be implemented using exclusiveOR and AND gates only. Draw the circuit.
AB'CD' + A'BCD' + AB'C'D + A'BC'D
Design a combinational circuit with three inputs x, y, and z, and three outputs, A, B, and C. When the binary input formed from xyz is 0, 1, 2, or 3, the binary output produced by ABC is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the input. Produce truth tables, and simplified algebraic forms, followed by circuits fot the simplified algebraic representations.
a. For the following Truth Table produce an algebraic representation for the outputs, f and g, in terms of the inputs a, b, c, and d.
a b c d  f g _____________ 0 0 0 0  0 1 0 0 0 1  1 1 0 0 1 0  0 0 0 0 1 1  0 0 0 1 0 0  0 1 0 1 0 1  0 1 0 1 1 0  0 0 0 1 1 1  0 0 1 0 0 0  1 0 1 0 0 1  0 0 1 0 1 0  0 0 1 0 1 1  1 0 1 1 0 0  0 0 1 1 0 1  0 0 1 1 1 0  0 0 1 1 1 1  1 1b. Draw a logic circuit that corresponds directly to the algebraic form.
a. Produce a truth table for a function f of four inputs, a, b, c, d that is 1 when the binary number abcd modulo 4 equals 1, and is 0 otherwise.
b. Produce the corresponding algebraic expression for f.
c. Draw a logic circuit that
corresponds directly to the algebraic form.
d.
Simplify the algebraic form for f .
e. Draw the logic circuit corresponding to the simplified form.
Submission:
• You may either type or neatly print
your solutions.
• Staple your
assignment answer sheets together with a standard computer science cover
sheet at the front and deposit into the handin box for the course. If the
number of sheets makes stapling difficult please use a 9x12 envelope with a Computer
Science cover page at the front to submit your assignment.