Question

Consider the three-place Boolean function f defined by the following rule: For each triple (x1, x2, x3) of 0's and 1's, f(x1, x2, x3) = (7x1 + 4x2 + 6x3) mod 2. (a) Find f(1, 1, 1) and f(0, 0, 1). f(1, 1, 1) = f(0, 0, 1) = (b) Fill in the blanks in the input/output table for f. Input Output x1 x2 x3 f 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0

          Consider the three-place Boolean function f defined by the following rule:
For each triple (x1, x2, x3) of 0's and 1's,
f(x1, x2, x3) = (7x1 + 4x2 + 6x3) mod 2.
(a) Find f(1, 1, 1) and f(0, 0, 1).
f(1, 1, 1) = 
f(0, 0, 1) = 
(b) Fill in the blanks in the input/output table for f.
Input Output
x1 x2 x3 f
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0

Consider the three-place Boolean function f defined by the following rule:
For each triple (x1, x2, x3) of 0's and 1's,
f(x1, x2, x3) = (7x1 + 4x2 + 6x3) mod 2.
(a) Find f(1, 1, 1) and f(0, 0, 1).
f(1, 1, 1) =
f(0, 0, 1) =
(b) Fill in the blanks in the input/output table for f.
Input Output
x1 x2 x3 f
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0

Added by Erica G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Eric Carlsen

01/11/2023

Step 1

According to the rule, we add the inputs and then take the result modulo 2. So, f(1, 1, 1) = (1 + 1 + 1) mod 2 = 3 mod 2 = 1. Show more…

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Consider the three-place Boolean function f defined by the following rule: For each triple (x1, x2, x3) of 0's and 1's, f(x1, x2, x3) = (7x1 + 4x2 + 6x3) mod 2. (a) Find f(1, 1, 1) and f(0, 0, 1). f(1, 1, 1) = f(0, 0, 1) = (b) Fill in the blanks in the input/output table for f. Input Output x1 x2 x3 f