Logic Gates & Boolean

Question 1

NAND gate

Question 2

NOR gate

Question 3

XOR gate

Question 4

XNOR gate

Question 5

what other representative is disjunctive normal form similar to

Answer 5

sum of products

Question 6

what other representative is conjunctive normal form similar to

Answer 6

product of sums

Question 7

how are expressions represented in DNF or SOP

Answer 7

C1 v C2 v C3 …

Question 8

how are clauses represented in DNF or SOP

Answer 8

L1 ^ L2 ^ L3 …

Question 9

what form is (A ^ ¬B ^ ¬ C) v (¬D ^ E ^ F) in

Answer 9

DNF

Question 10

what form is AB + C in

Answer 10

SOP

Question 11

how to convert to DNF or SOP

Answer 11

• use a truth table
• pick out rows where output is 1
• if input is row is 0, negate the corresponding variable

Question 12

how are expressions represented in CNF or POS

Answer 12

C1 ^ C2 ^ C3 …

Question 13

how are clauses represented in CNF or POS

Answer 13

L1 v L2 v L3

Question 14

what form is (A v ¬B v ¬C) ^ (¬D v E v F) in

Answer 14

CNF

Question 15

what form is (A + B).C in

Answer 15

POS

Question 16

how to convert to CNF or POS

Answer 16

• use truth table
• pick out rows where the output is 0
• if input in row is 1, negate the corresponding variable

Question 17

name the 7 combinational logic circuits

Answer 17

1. multiplexor
2. demultiplexor
3. decoder
4. ROM
5. Adder
6. Half-adder
7. Mulit-bit adders

Question 18

what is a multiplexor

Answer 18

• selector
• one of the inputs will be the output by using signal input bits
• USES: program counter - control routing of data or signals

Question 19

what is a demultiuplexor

Answer 19

• selects output path by using signal input bits
• opposite to multiplexor

Question 20

what is a decoder

Answer 20

• circuit with n inputs & 2^n outputs
• determines output line based on inputs
• USES: address decoding & address space

Question 21

how is ROM a combinational logic circuit

Answer 21

• can be implemented as a decoder and OR gates
• decoder selects address
• four outputs give 4-bit value stored there

Question 22

draw a half adder

Question 23

draw a full adder

Question 24

how to make a 4-bit adder

Answer 24

4 x 1-bit adders

Question 25

how to make a 32-bit adder

Answer 25

4 x 8-bit full adders

Question 26

name the 9 sequential logic circuits

Answer 26

1. flip flops 2. S-R latch 3. clocked S-R latch 4. D flip flop 5. J-K flip flop 6. register 7. counter 8. ripple counter 9. synchronous counter

Question 27

what is a flip flop

Answer 27

1. it exists in one of two states and, in the absence of an input remains in that state 2. functions as a 1-bit memory 3. 2 outputs, which are always the complements of each other

Question 28

what is an S-R latch

Answer 28

simple flip flop - s = set bit, r = reset bit

Question 29

draw an S-R latch

Question 30

draw and S-R characteristic table

Question 31

what is the difference with a clocked S-R latch

Answer 31

- synchronises to clock pulse - useful to have in a system where we can predict the state change

Question 32

draw a clocked S-R latch

Question 33

what is a D flip flop

Answer 33

- implemented as a single input - avoids SR 11 invalid input

Question 34

draw a D flip flop

Question 35

draw a D flip flop characteristic table

Question 36

what is a J-K flip flop

Answer 36

- all possible inputs are valid

Question 37

draw a J-K flip flop

Question 38

draw a J-K flip flop characteristic table

Question 39

what is a register in terms of sequential logic circuits

Answer 39

- example of a use of flip flops

Question 40

types of register implementation

Answer 40

1. parallel 2. shift

Question 41

what is the parallel implementation of a register

Answer 41

- set of 1-bit memory items - can be read & written to concurrently

Question 42

what is the shift implementation of a register

Answer 42

- data inputs from the left - with each clock pulse, data shifts right & rightmost bit is output

Question 43

what is a counter in terms of sequential logic circuits

Answer 43

- register whose value is incremented by 1 - after max value achieved, register is reset to 0

Question 44

what is a ripple counter

Answer 44

- asynchronous - signal to increment starts at one end and 'ripples' through - J & K are inputs - when clock pulses, counter is incremented by 1

Question 45

what is a synchronous counter

Answer 45

- flip flops change at the same time