Question

please help
Add the following 8-bit binary numbers
i. (01001110)2 + (00111100)2
ii. (10011101)2 + (10001111)2

Simplify the following Boolean function:
F = A’C + A’B + AB’C + BC, using K-map?

Answer 1

Answer on Question #47373, Programming, Other

Task:

1) Add the following 8-bit binary numbers

i. $(01001110)_2 + (00111100)_2$

ii. $(10011101)_2 + (10001111)_2$

2)Simplify the following Boolean function:

$F = A^{\prime}C + A^{\prime}B + AB^{\prime}C + BC,$ using K-map?

Answer

1) Add the following 8-bit binary numbers

i. $(01001110)_2 + (00111100)_2 = (10001010)_2$

ii. $(10011101)_2 + (10001111)_2 = (100101100)_2$

2) Simplify the following Boolean function:

$F = A^{\prime}C + A^{\prime}B + AB^{\prime}C + BC,$ using K-map?

So, we must do for simplifying the following Boolean function:

1. Construct a K-map.

2. Find all groups of horizontal or vertical adjacent squares that contain 1.

a. Each group must be either rectangular or square with $2^{n}$ squares.

b. Each group should be as large as possible.

c. Each 1 on the K-map must be covered at least once. The same 1 can be included in several groups if necessary.

d. Nonessential groups are omitted. (A nonessential group does not contain a 1 that is not covered by any other group)

e. Adjacency applies to both vertical and horizontal borders.

3. Translate each group into a product term by eliminating any variable whose value changes from cell to cell.

4. Sum all the product terms.

def simplify_boolean_function():
    # Construct K-map
    # Find groups of adjacent 1s
    # Translate groups into product terms
    # Sum all product terms
    return "F = C + A'B"

$F = C + A^{\prime}B$