Assignment (3-6) Boolean Algebra and Logic Simplification - General Questions

Size: px

Start display at page:

Download "Assignment (3-6) Boolean Algebra and Logic Simplification - General Questions"

Giles Hicks
6 years ago
Views:

1 Assignment (3-6) Boolean Algebra and Logic Simplification - General Questions 1. Convert the following SOP expression to an equivalent POS expression. 2. Determine the values of A, B, C, and D that make the sum term equal to zero. A = 1, B = 0, C = 0, D = 0 A = 1, B = 0, C = 1, D = 0 A = 0, B = 1, C = 0, D = 0 A = 1, B = 0, C = 1, D = 1 3. Which of the following expressions is in the sum-of-products (SOP) form? (A + B)(C + D) (A)B(CD) AB(CD) AB + CD 4. Derive the Boolean expression for the logic circuit shown below:

2 5. From the truth table below, determine the standard SOP expression. 6. One of De Morgan's theorems states that. Simply stated, this means that logically there is no difference between: a NOR and an AND gate with inverted inputs a NAND and an OR gate with inverted inputs an AND and a NOR gate with inverted inputs a NOR and a NAND gate with inverted inputs 7. The commutative law of Boolean addition states that A + B = A True False 8. Applying DeMorgan's theorem to the expression, we get. 9. The systematic reduction of logic circuits is accomplished by: using Boolean algebra symbolic reduction TTL logic using a truth table

3 10.Which output expression might indicate a product-of-sums circuit construction? 11.An AND gate with schematic "bubbles" on its inputs performs the same function as a(n) gate. NOT OR NOR NAND 12.For the SOP expression column?, how many 1s are in the truth table's output A truth table for the SOP expression has how many input combinations? How many gates would be required to implement the following Boolean expression before simplification? XY + X(X + Z) + Y(X + Z) Determine the values of A, B, C, and D that make the product term equal to 1. A = 0, B = 1, C = 0, D = 1 A = 0, B = 0, C = 0, D = 1 A = 1, B = 1, C = 1, D = 1 A = 0, B = 0, C = 1, D = 0 16.How many gates would be required to implement the following Boolean expression after simplification? XY + X(X + Z) + Y(X + Z) 1

4 AC + ABC = AC True False 18. When are the inputs to a NAND gate, according to De Morgan's theorem, the output expression could be: X = A + B X = (A)(B) 19.Which Boolean algebra property allows us to group operands in an expression in any order without affecting the results of the operation [for example, A + B = B + A]? associative commutative Boolean distributive 20. Applying DeMorgan's theorem to the expression, we get 21.When grouping cells within a K-map, the cells must be combined in groups of. 2s 1, 2, 4, 8, etc. 4s 3s 22.Use Boolean algebra to find the most simplified SOP expression for F = ABD + CD + ACD + ABC + ABC F = ABD + ABC + CD F = CD + AD F = BC + AB F = AC + AD 23.Occasionally, a particular logic expression will be of no consequence in the operation of a circuit, such as a BCD-to-decimal converter. These result in terms in the K-map and

5 can be treated as either or, in order to the resulting term. don't care, 1s, 0s, simplify spurious, ANDs, ORs, eliminate duplicate, 1s, 0s, verify spurious, 1s, 0s, simplify 24.The NAND or NOR gates are referred to as "universal" gates because either: can be found in almost all digital circuits can be used to build all the other types of gates are used in all countries of the world were the first gates to be integrated 25.The truth table for the SOP expression has how many input combinations? Converting the Boolean expression LM + M(NO + PQ) to SOP form, we get. LM + MNOPQ L + MNO + MPQ LM + M + NO + MPQ LM + MNO + MPQ 27.A Karnaugh map is a systematic way of reducing which type of expression? product-of-sums exclusive NOR sum-of-products those with overbars 28. The Boolean expression is logically equivalent to what single gate? NAND NOR AND OR 29.Applying the distributive law to the expression, we get.

6 30.Mapping the SOP expression, we get. (A)

7 (B) (C) (D) 31.Derive the Boolean expression for the logic circuit shown below: 32.Which is the correct logic function for this PAL diagram? 33.For the SOP expression, how many 0s are in the truth table's output column? zero Mapping the standard SOP expression, we get

8 (A) (B) (C) (D)

9 35.Which statement below best describes a Karnaugh map? A Karnaugh map can be used to replace Boolean rules. The Karnaugh map eliminates the need for using NAND and NOR gates. Variable complements can be eliminated by using Karnaugh maps. Karnaugh maps provide a cookbook approach to simplifying Boolean expressions. 36.Applying DeMorgan's theorem to the expression, we get. 37.Which of the examples below expresses the distributive law of Boolean algebra? (A + B) + C = A + (B + C) A(B + C) = AB + AC A + (B + C) = AB + AC A(BC) = (AB) + C 38. Applying DeMorgan's theorem to the expression, we get. 39.Which of the following is an important feature of the sum-of-products (SOP) form of expression? All logic circuits are reduced to nothing more than simple AND and OR gates. The delay times are greatly reduced over other forms. No signal must pass through more than two gates, not including inverters. The maximum number of gates that any signal must pass through is reduced by a factor of two. 40.An OR gate with schematic "bubbles" on its inputs performs the same functions as a(n) gate. NOR OR NOT NAND 41.Which of the examples below expresses the commutative law of multiplication? A + B = B + A AB = B + A

10 AB = BA AB = A B 42.Determine the binary values of the variables for which the following standard POS expression is equal to 0. ( )( ) ( )( ) ( )( ) ( )( ) 43.The expression W(X + YZ) can be converted to SOP form by applying which law? associative law commutative law distributive law none of the above 44.The commutative law of addition and multiplication indicates that: we can group variables in an AND or in an OR any way we want an expression can be expanded by multiplying term by term just the same as in ordinary algebra the way we OR or AND two variables is unimportant because the result is the same the factoring of Boolean expressions requires the multiplication of product terms that contain like variables 45. Which of the following combinations cannot be combined into K-map groups? corners in the same row corners in the same column diagonal overlapping combinations

Summary. Boolean Addition

Summary. Boolean Addition Summary Boolean Addition In Boolean algebra, a variable is a symbol used to represent an action, a condition, or data. A single variable can only have a value of or 0. The complement represents the inverse