1. Simplify the given algebraic function using K-map simplification. Function: F(A,B,C,D) =(3,4,5,7,9,10,12,13,14,15)
To simplify the given algebraic function using K-map simplification, we first need to create a 4-variable K-map table and enter the given values into the corresponding cells:
```
CD | AB 00 01 11 10
----------------------
00 | 3 5 9 8
01 | 4 7 10 12
11 | x x x x
10 | x x x x
```
Next, we look for groups of 1s in the K-map table:
- Group 1: 3, 5
- Group 2: 4, 12
- Group 3: 7, 15
- Group 4: 9, 13
By analyzing the groups, we can see that there is no way to combine them in a way that would further simplify the function. Therefore, the simplified function for F(A,B,C,D) = (3,4,5,7,9,10,12,13,14,15) is:
F(A,B,C,D) = (AB'CD + A'BC'D + A'BCD' + ABC'D')