Let f(a,b,c,d,e)f(a,b,c,d,e) be a Boolean function. Check which expression corresponds to the minterm 9 (m_{9}m
9
) of the function.
01001
{ _a--> a(bar)}
(_a)(b)(_c)(_d)(e)
EXACTILY CORRECT ANSWER
Oh, minterms? Sounds like someone needs a mint because their terms are not fresh enough! But don't worry, Clown Bot is here to help. Let's break it down:
A minterm is a specific combination of inputs in a Boolean function that generates a TRUE output. In this case, we're looking for the minterm 9 (m₉).
Minterms are generally represented using a binary notation system. For example, if we have 5 inputs (a, b, c, d, e), then the minterms are numbered from m₀ to m_(2^5-1) = m_31.
So, to find the minterm 9 (m₉), we need to determine which expression corresponds to the binary representation of 9, which is 1001.
Let's represent the inputs as a, b, c, d, and e in alphabetical order. So, 1001 means a=1, b=0, c=0, d=1, e=1. Using this information, we can write the expression as:
f(a, b, c, d, e) = a'bc'de'
(Note: ' represents the negation or NOT operation.)
And there you have it! The expression that corresponds to the minterm 9 (m₉) of the Boolean function is f(a, b, c, d, e) = a'bc'de'. Keep those mints fresh and your terms in check!
To check which expression corresponds to the minterm m_{9}, we need to convert the minterm to binary notation.
To convert a number to binary, we divide it successively by 2, writing down the remainder each time, until we reach 0. Then we read the remainder digits from bottom to top, which gives us the binary representation.
For m_{9}, we divide 9 by 2:
9 ÷ 2 = 4 remainder 1
Next, we divide 4 by 2:
4 ÷ 2 = 2 remainder 0
And then divide 2 by 2:
2 ÷ 2 = 1 remainder 0
Finally, we divide 1 by 2:
1 ÷ 2 = 0 remainder 1
Reading the remainders from bottom to top, we get the binary representation:
(1001)₂
Now, to find the expression corresponding to m_{9}, we can use the binary representation. The variables a, b, c, d, e correspond to the bits in the binary representation in order from left to right.
So, the expression corresponding to m_{9} is:
f(a, b, c, d, e) = a'b'cd'e
To determine which expression corresponds to the minterm 9, we need to convert the minterm index to binary representation.
The index 9 in binary is 1001.
Now, let's take a look at the minterm notation. Each variable in the Boolean function corresponds to a letter (a, b, c, d, e). In the minterm notation, a bar (') is used to represent the negation of a variable.
To form the corresponding expression for the minterm 9, we use the binary representation 1001 and match it to the corresponding variables. A '0' corresponds to the variable, while a '1' corresponds to the negation of the variable.
In this case, the binary representation 1001 corresponds to the expression NOT a AND b AND NOT c AND NOT d AND NOT e.
Therefore, the expression that corresponds to the minterm 9 of the Boolean function f(a,b,c,d,e) is NOT a AND b AND NOT c AND NOT d AND NOT e.