Chapter 43 - Adders and D-type flip-flops

Question 1

Is it possible to output the results of a binary addition or subtraction?

Answer 1

» Yes with the right combination of gates

Question 2

What is a half adder?

Answer 2

» An adder performs binary addition and subtraction

Question 3

What is the purpose of a half adder?

Answer 3

» Performs addition of 2bits

Question 4

How many inputs and outputs does a half adder produce?

Answer 4

» Takes an input of 2 bits of A and B and outputs results S and carry C

Question 5

What gates does a half-adder consist of?

Answer 5

» XOR gate
» AND gate

Question 6

What does S represent?

Answer 6

» The sum and is equal to A XOR B

Question 7

What does C represent?

Answer 7

» Represents the Carry and is equal to A AND B

Question 8

What are the disadvantages of a half adder?

Answer 8

» Can only add one bit
» No third input so cannot use the carry from a previous addition to add n bit numbers

Question 9

If A and B was both 1, what is the value of S and C in a half adder?

Answer 9

» S = 0
» C = 1

Question 10

What is a full adder?

Answer 10

» Consists of 2 half adders to add three bits together including the inputs A and B and a Carry bit

Question 11

How many inputs and output does a full adder have?

Answer 11

» Has 3 inputs, A, B, and C(in)
» 2 outputs, the SUM(S) and C(out)

Question 12

What gates does the full adder consist of?

Answer 12

» 2 XOR GATES
» 2 AND GATES
» 1 OR GATE
» 2 half adders and 1 OR

Question 13

What is the boolean logic of S and C(out) in a full adder?

Answer 13

» S = (A XOR B) XOR C(in)
» C(out) = ((A XOR B) AND C ) OR ( A AND B)

Question 14

What does concatenating full adders do?

Answer 14

» Can be connected to make n full adders
» Can input the carry bit into a subsequent adder along with the 2 new inputs

Question 15

How can you simply add the adders together?

Answer 15

» Draw a diagram, with A0, B0, S0 and so on
» Then simply add the values and where appropriate carry a single bit

Question 16

What is a flip flop?

Answer 16

» An elemental sequential logic circuit that can store on bit and flip between 2 states, 0 and 1

Question 17

» How many inputs does a D - Type flip flop have?

Answer 17

» 2 inputs one called D
» Other one called clock signal input

Question 18

What is the clock?

Answer 18

» Or also known as the oscillator is another type of sequential circuit that changes state at regular time intervals

Question 19

Why is the clock needed?

Answer 19

» Needed to synchronise the change of state of flip flop circuit

Question 20

What is the clock perod?

Answer 20

» The time between the 2 rising edge

Question 21

What is the clock width?

Answer 21

» The width between the rising edge, and falling edge

Question 22

When can the D- type flip flop only change states?

Answer 22

» Changes on the rising edge of of the clock signal

Question 23

What does the D stand for in D-type flip flop?

Answer 23

» D stands for Data or Delay

Question 24

What does it mean by a positive edge triggered flip flop?

Answer 24

» Can only change the output value from 1 to 0

Question 25

What happens when the clock is not a positive edge?

Answer 25

» The input value is held and does not change

Question 26

Why is a D-type flip flop important?

Answer 26

» Can be used as a memory cell to store the state of a bit

Question 27

When does the output Q take a new value?

Answer 27

» When the value at D has changed at the point of a clock pulse » This means the clock pulse will freeze or store the input value of D until the next clock pulse

Question 28

What are the uses of the D-type flip flops?

Answer 28

» Creating registers and counters » Used for intermediate storage needed using arithmetic operations

Question 29

What is Static RAM?

Answer 29

» RAM that is created using several D-Type flip flops

Question 30

» What are the advantages of SRAM?

Answer 30

» Much faster then DRAM - Dynamic RAM

Question 31

What are the disadvantages of SRAM?

Answer 31

» More expensive then DRAM

Question 32

What is SRAM and DRAM used for?

Answer 32

» SRAM used for cache memory » DRAM used for main memory

Question 33

How many flip flops are required to store 8 - bits?

Answer 33

» 8 flip flops

Question 34

Describe how the clock signal in a D type flip flop works?

Answer 34

» Clock signal is a regular steady pulse used by a CPU to time operations » Output Q can only be altered at the beginning of a clock signal » Change to Q will only occur if D is in a different state to what it was at the start of the previous clock signal

Question 35

What binary operation is performed by adders?

Answer 35

» Addition

Question 36

Explain what a Full adder circuit does

Answer 36

» This circuit consists of 2 half adders, and is called a full adder. » It has 3 inputs called A, B and C(in), A and B are the inputs from the computer, and C(in) is the carry bit. » This logic circuit produces the sum of A, B and Cin using XOR gates, the sum is then stored in a seperate memory location. » C, out is the carry bit and in the next fuller adder it will be represented as Cin, C, out is the carry bit from the 3 inputs of A, B and Cin