1.4.3 Boolean Algebra

Question 1

D-Type flip flops

Answer 1

• is a logic circuit which can store the value of one bit (0 or 1)
• has two inputs
• D : a single-bit data input
• CLK : a clock signal
• also has two outputs
• Q : a single bit data output
• ‘Q : the inverse of the data output

Question 2

Clock signal

Answer 2

• is a regular pulse (change in voltage) generated by the CPU which is used to coordinate the computers components
• in the D type flip flop the clock signal determines when data is captured and stored

Question 3

Storing a single bit using D type flip flops

Answer 3

• a clock pulse rises and falls ( rising and falling edge )
• the value of a d type flip flop (Q) can only change at a rising edge (the start of a clock tick )
• the value of Q is updates to the value of D where the clock (CLK) rises
• the value/state of Q is the stored value
• if the clock is not at a rising edge the output value (Q) is held and doesn’t change

Question 4

Use case of D type flip flops

Answer 4

• Memory Storage: Temporary data storage in processors (e.g., registers).
• Counters: Implementing binary counters.
• Shift Registers: Shifting data bits in serial communication.
- data synchronisation

Question 5

Adder circuits

Answer 5

• Logic circuits that add bits together
• there are two types of adders :
• full adder
• half adder

Question 6

Half adder

Answer 6

• used to perform the addition of 2 single bit numbers
• has only 2 inputs A and B (the bits to be added)
• has two outputs Sum (S) and Carry (C out)
• formed from two logic gates AND and XOR

Question 7

Full adder

Answer 7

• similar to half adder but has 3 inputs instead
• A, B, and an (C in) (carry input from a previous stage)
• which allows a cat to be represented
• produces two outputs C out and Sum (S)
• two half adder can be joined with an OR gate to form a full adder [1]

Question 8

Describe how a half adder can be adapted to add together two 4 bit binary numbers

Answer 8

• half adder adds together 2 binary digits (bits) [1]
• S gives the Sum and C gives the carry [1]
• 2 half adders can be joined together with an OR gate [1]
• to form a full adder [1]
• 4 full adders can be used to add two 4 bit numbers ( forming a ripple adder) [1]
• carry output in one full adder joined to the carry input on the next stage