# Truth Table of a funtion ,, HELP

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#### IronMan2010

##### New Member
The Function is F=(x+1)²+xy where x is two bits variable and y is one bit variable

How can i make truth table of this Function where x is two bits ??? i mean when the inputs are 1 1 1 ??? a little help pls ?

#### MikeMl

##### Well-Known Member
Let x = 2*m+n, where m, n. and y are either 0 or 1. (hint, there will be 2^3 states in the table)

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#### Ratchit

##### Well-Known Member
IronMan2010,

Let x = 2*m+n, where m, n. and y are either 0 or 1. (hint, there will be 2^3 states in the table)
Are we discussing Boolean algebra here? How can a expression be squared or a term have more than one value?

Ratch

#### IronMan2010

##### New Member
Sorry Mike,, Why x=2*m+n ???

#### IronMan2010

##### New Member
IronMan2010,

Are we discussing Boolean algebra here? How can a expression be squared or a term have more than one value?

Ratch
I will tell the whole problem, Design a ROM To store the equation F=(x+1)²+xy
where x is two bits variable, and y is single bit variable.

SO i want to find the truth table of this Function... Or at least that's what i have in mind,, what say you ?

#### Ratchit

##### Well-Known Member
IronMan2010,

SO i want to find the truth table of this Function... Or at least that's what i have in mind,, what say you ?
OK, here is my take on the problem. The highest value of the function is 19, so the ROM must have a 5-bit memory, unless there some bits in common with all the values of the function. The function can be simplied to x(x+y+2)+1 . x can 4 different values and y can have 2 different values. That means 4x2=8 different function values. The truth table is shown below.

Code:
x    y    f
-----------
00   0    1
00   1    1
01   0    4
01   1    5
10   0    9
10   1    11
11   0    16
11   1    19
Ratch

#### MikeMl

##### Well-Known Member
Sorry Mike,, Why x=2*m+n ???
So x can take on the value of 3,2,1, or 0. (e.g. with m=1, n=0, so x = 2*1 + 0 = 2), which is what Ratch did.

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#### IronMan2010

##### New Member
Thank you guys,, you were much of a Help

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