# Implementing a circuit with a decoder

Discussion in 'Homework Help' started by mcc123pa, Dec 5, 2010.

1. ### mcc123pa Thread Starter Member

Sep 12, 2010
40
0
Hello-

Here are the directions to the problem that I am stumped on:

A combinational circuit is specified by the following Boolean function:
F(A,B,C,D) = Ʃ(0,2,6,7,8)

A) Implement the circuit with a decoder and external gates.

Below is my attempt at a solution:

step 1: I transfer this expression to a four variable K-map and get the following optimized expression:
f= b'c'd+a'cd'+a'bc

step 2: I have to introduce all four variables to each term so I perform the following expansion:

F= b'c'd'(a+a')+a'cd'(b+b')+a'bc(d+d')
F= ab'c'd'+a'b'c'd'+ a'bcd'+a'b'cd'+a'bcd+a'bcd'
(8) (0) (6) (13) (7) (6)

step 3: I set up the decoder with the external OR gate and connect outputs 8, 0, 6, 13, and 7 to it.

My question is, did I do it correct up to here? If I did, should I connect 6 to the OR gate twice? Or do I need to look in a new direction to finish this problem? Please advise either way. Thanks in advance for your answers!!

2. ### blah2222 Well-Known Member

May 3, 2010
565
33
Yeah, that's right. Since the question didn't specify what type of decoder to use, you can just assume a 4:16 decoder with an enable input. Since the function is true at minterms: 0, 2, 6, 7, and 8, just hook all the corresponding output wires up into an OR gate, and don't connect the other outputs, leaving them with high impedance outputs.

3. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
What you did there was totally meaningless. You started from the minterms stated as a sum, got them through a K-map, simplified it and re-expanded them, just to get to them again and wrong too?!

Just hook up your OR gate in the decoder's outputs 0,2,6,7,8 as your problem initially states.

4. ### mcc123pa Thread Starter Member

Sep 12, 2010
40
0
Thanks for the replies and help everyone!!