Digital Logic Design

Question 1

What does binary logic consist of?

Answer 1

• Binary Variables (letters that represent either 1 or 0)

- Logical operations (AND, OR, NOT)

Question 2

What is the notation for AND?

Answer 2

x⋅y

Question 3

What is the notation for OR?

Answer 3

x+y

Question 4

What is the notation for NOT?

Answer 4

x’ or x̄

Question 5

What is the switching circuit convention?

Answer 5

Open switch = 0

Closed switch = 1

Question 6

What is the solid state circuit convention?

Answer 6

Logic 1 is represented with a high voltage
Typically 3.3V or 5V (approximately)

Logic 0 is represented with a low voltage
Usually 0V (approximately)

**Note values on pg 32 in textbook, has to be around 0 and around 3.3 not exactly those numbers

Question 7

What does the AND symbol gate look like?

Answer 7

Check white binder

Question 8

What does the OR symbol gate look like?

Answer 8

Check white binder

Question 9

What does the NOT symbol gate look like?

Answer 9

Check white binder

Question 10

What are the basic rules of boolean algebra?

Answer 10

Has a set of two elements. B = {0.1}
Has the two binary operators · and + (AND and OR)
Their results are strictly defined (can only be 0 or 1)

Question 11

What are the basic postulates of boolean algebra?

Answer 11

• Closed with respect to + and ·
  The result of these operations is always 0 or 1
• The identity element for + is 0
  x + 0 = 0 + x = x
• The identity element for · is 1
  x · 1 = 1 · x = x
• Commutative with respect to + and ·
  x + y = y + x
• · is distributive over +
  x · (y+z) = (x · y) + (x · z)
• • is distributive over ·
    x + (y · z) = (x+y) · (x + z)
• For every x there exists a complement x’ that satisfies the rules x + x’ = 1 and x · x’ = 0
• There are at least two elements x and y in the set of elements B such that x != y