#### arran1987

Joined Apr 19, 2007
2
Hi i have been asked to:

produce a logic circuit design that satisfies the logic conditions shown in the truth table below.
write down the boolean expression for the outputs of the truth table.
identify the type of logic gates used in your design

here is the truth table ab&c are the inputs and Q is the outputs.

A B C Q

0 0 0 0

1 0 0 1

0 1 0 0

1 1 0 1

0 0 1 0

1 0 1 1

0 1 1 1

1 1 1 1

ANY IDEAS THANKS

IF IT IS HARD TO TYPE SEND A SCANNED HAND WRITTEN PAGE TO

arranscotter@yahoo.co.uk

thanks again

#### Papabravo

Joined Feb 24, 2006
20,603
The brute force approach is to use a 3-input AND gate for each line in the truth table for which Q=1. There are five of them. Then use a 5-input OR gate to combine the 5 minterms.

The boolean expression is the logical sum (OR) of the 5 terms. It may also be possible to simplify the expression.

An even slicker way to do the problem is to use an 8:1 multiplexer with A, B, and C connected to the select inputs, and the values of the output connected to the data inputs.

#### Dave

Joined Nov 17, 2003
6,969
What have you done so far on this?

If the answer is nothing, I suggest you firstly look at how you can translate the truth table into a boolean expression. Then simplify the expression. What do you get?

We will help you, but ultimately you are expected to do the work.

Dave

#### Dave

Joined Nov 17, 2003
6,969
The brute force approach is to use a 3-input AND gate for each line in the truth table for which Q=1. There are five of them. Then use a 5-input OR gate to combine the 5 minterms.

The boolean expression is the logical sum (OR) of the 5 terms. It may also be possible to simplify the expression.

An even slicker way to do the problem is to use an 8:1 multiplexer with A, B, and C connected to the select inputs, and the values of the output connected to the data inputs.
I think the aim/approach for the homework is to write the truth table as a Boolean function, simplify and then translate the expression into a discrete gate circuit. Thats said your appraoch is equally valid, the OP should clarify this point before proceding.

Dave

#### arran1987

Joined Apr 19, 2007
2
still no idea how to get the boolean expression #### Dave

Joined Nov 17, 2003
6,969
still no idea how to get the boolean expression Where there is a 1 in the Q column, write the corresponding A,B,C combination. For example:

A-B-C-Q
1-0-0-1

Would be A.B'.C' (where ' denotes a NOT).

You need to do this for all cases where Q = 1. Once you have all these expressions you bring them together into a full expression using the OR operator.

Make sense?

Dave

#### recca02

Joined Apr 2, 2007
1,212
isnt using kernaugh map a good alternative.
it gives a quicker answer for expression and reduces the components req.
i wud solve this one for u in case req but first please let us know how far have u gone with the task.