- #1
peripatein
- 880
- 0
Hi,
I'd like to find Bθ:{0,1}3→{0,1}2 which is defined as follows:
Input: x,y,z[itex]\in[/itex]{0,1},
Output: s,c[itex]\in[/itex]{0,1},
Functionality:2c+s=x+y+z
I first tried listing all the possible combinations of x,y,z, and there are obviously 8. I noted that x+y+z would yield 1 only if at least one of the three were one. I then tried to find a Boolean formula for s and one for c, so I could use the relation given in the "functionality" above, but I truly got lost. How may I possibly assign a function to s and c? There certainly could be more than one such function satisfying that equation, couldn't there? In any case, I'd sincerely be thankful for some guidance/advice.
Homework Statement
I'd like to find Bθ:{0,1}3→{0,1}2 which is defined as follows:
Input: x,y,z[itex]\in[/itex]{0,1},
Output: s,c[itex]\in[/itex]{0,1},
Functionality:2c+s=x+y+z
Homework Equations
The Attempt at a Solution
I first tried listing all the possible combinations of x,y,z, and there are obviously 8. I noted that x+y+z would yield 1 only if at least one of the three were one. I then tried to find a Boolean formula for s and one for c, so I could use the relation given in the "functionality" above, but I truly got lost. How may I possibly assign a function to s and c? There certainly could be more than one such function satisfying that equation, couldn't there? In any case, I'd sincerely be thankful for some guidance/advice.