1.4.3 Boolean Algebra

Question 1

What are adders useful for?

Answer 1

Outputting the results of binary addition and subtraction.

Question 2

How many inputs does a half adder take?

Answer 2

Two

Question 3

How many outputs does a half adder produce?

Answer 3

2

Sum and carry bit

Question 4

What logic gates is a half adder made up of?

Answer 4

AND gate

XOR gate

Question 5

What is the issue with half adders?

Answer 5

They only output the carry bit and do not use it in the addition.

Question 6

What does a full adder combine?

Answer 6

Two half adders.

Question 7

What is the boolean expression for the sum output from a half adder?

Answer 7

S = A ⊻ B

Question 8

What is the boolean expression for the carry bit output from a half adder?

Answer 8

C = A ∧ B

Question 9

What does a full adder allow for?

Answer 9

The input of the carry from the last calculation into the next calculation.

Question 10

How many inputs does a full adder accept?

Answer 10

3

A, B and carry bit from previous

Question 11

How many outputs does a full adder produce?

Answer 11

2

Sum and carry bit

Question 12

What logic gates is a full adder made up of?

Answer 12

2 x Half adder (AND + XOR)

OR gate

Question 13

What is the boolean expression for the sum output from a full adder?

Answer 13

S = A ⊻ B ⊻ Cᵢₙ

Question 14

What is the boolean expression for the carry bit output from a full adder?

Answer 14

Cₒᵤₜ = (A ∧ B) v (Cᵢₙ ∧ (A ⊻ B))

Question 15

How many full adders do we need to add together two binary numbers, n bits long?

Answer 15

n full adders.

Question 16

What is a D-type flip-flop?

Answer 16

A sequential logic circuit that can store one bit and flip between two states.

Question 17

What are the inputs into a D-type flip-flop?

Answer 17

A control input = D

Clock signal

Question 18

When will a D-type flip flop only change the output value?

Answer 18

When the clock is at a rising edge.

Question 19

What happens when the clock is not at a positive edge?

Answer 19

The input value does not change.

Question 20

What is the use of a D-type flip-flop?

Answer 20

It can be used as a memory circuit to store the state of a bit.