Let f(a,b,c,d,e) be a Boolean function. Check which expression corresponds to the minterm 19 (m19) of the function.
a.b.c.d.e
a¯.b.c¯.d¯.e
a.b¯.c¯.d.e
a.b¯.c¯.d.e¯
Let be a Boolean function. Check which expression corresponds to the minterm 16 (m16) of the function.
Last one is correct
Well, let's see. The minterm 19 (m19) means that the variables a, b, c, d, and e are all true. So, looking at the given options:
a.b.c.d.e - This expression is true when all variables are true, so it corresponds to m19.
a¯.b.c¯.d¯.e - This expression is true when a, c, and d are false, and b and e are true. So, it does not correspond to m19.
a.b¯.c¯.d.e - This expression is true when a, d, and e are true, and b and c are false. So, it does not correspond to m19.
a.b¯.c¯.d.e¯ - This expression is true when a, d, and c are true, and b and e are false. So, it does not correspond to m19.
Therefore, the expression that corresponds to m19 is a.b.c.d.e. It seems like all the other options are just clowning around!
To determine which expression corresponds to the minterm 19 (m19) of the Boolean function f(a,b,c,d,e), we need to convert the minterm number to its binary representation and match it with the corresponding variables.
The binary representation of 19 is 10011.
So, we need to look for an expression that has a,b,c, d, and e in the following pattern - a.b.c¯.d.e
Out of the given expressions, the one that matches is:
a.b.c¯.d.e
Therefore, the expression that corresponds to the minterm 19 (m19) is a.b.c¯.d.e.
To determine the expression that corresponds to the minterm 19 (m19), we need to find the combination of variables that satisfies the minterm. Each variable can exist in either complemented form (with an overline, ¯) or non-complemented form.
Here is the step-by-step process to check which expression corresponds to m19:
1. Assign the minterm value to the variables: In this case, m19 is 19 in decimal, which corresponds to 10011 in binary. Assign each binary digit to the corresponding variable. Let's use a, b, c, d, and e to represent each digit.
2. Determine the complemented/non-complemented form: Read each digit from left to right and apply the complemented/non-complemented form accordingly.
- For a: Since the first digit is 1, use a in complemented form (a¯).
- For b: The second digit is 0, so use b in non-complemented form (b).
- For c: The third digit is 0, so use c in non-complemented form (c).
- For d: The fourth digit is 1, so use d in complemented form (d¯).
- For e: The fifth digit is 1, so use e in non-complemented form (e).
3. Write the expression: Combine the variables using AND (.) or OR (+) operations.
The expression corresponding to m19 is:
a¯.b.c.d¯.e
Thus, the correct option is a¯.b.c.d¯.e.