cspp topic 2

what is a truth table?

a table that lists all possible input combinations and their corresponding output values, to define the behaviour of a logic function

what is using two switches in series the logical equivalent of?

AND

what is the logical equivalent of using two switches in parallel?

OR

what is an advantage of K-maps?

reduces the need for a lot of calculation, uses simple pattern recognition ability in us

how does k-map work?

groups adjacent 1s to form simplified product terms

what does larger groups in a kmap mean?

more simplification

what is gray code in k-maps?

the specific ordering of variables along the rows and columns such that only one-bit changes between adjacent cells

why is gray coding used in k-maps?

to ensure that adjacent cells represent minterms that differ by only one variable

when are k-map cells considered adjacent?

if they differ by only one variable (ie. their binary representations differ by only one bit)

what is a don’t care state?

an input combination where the output can be 0 or 1, where it does not matter for real-world operation of the circuit

what is the benefit of having don’t care states?

allows us to create simpler logic expression, as we can conclude that these cases are irrelevant or will never occur, so we can treat them as 0 or 1 to simplify the expressions

what are combinational logic circuits?

digital circuits where the output depends only on the current input values

what is an adder?

a digital circuit that performs addition operation on binary numbers, found inside the ALU

what purpose do adders serve in the ALU?

used to calculate addresses, table indices, and similar operations

what are the 5 types of adders?

half adder, full adder, ripple adder, look ahead carry unit, carry-save adder

what does a 1-bit half adder do?

performs the addition of two bits

what does a 1-bit full adder do?

adds 3 inputs together, 3rd input can be the carry over from the previous half adder

how can an n-bit full adder be created?

using the same logic of two half adders in series, with n half adders

how can an adder be converted into an adder/subtractor?

add a control input Z such that

• when Z = 0, S = A+B

• when Z = 1, S = A-B

how can we calculate (-B) using two’s complement?

invert the n-bit binary number B by finding Z XOR B, use Z as the carry-in of the adder

what is active high?

a state in a control signal if the signal performs its intended purpose when the voltage level is high (logic - 1)

what is active low?

a state in a control signal if the signal performs its intended purpose when the voltage level is low (logic - 0)

how dos a multiplexer work?

routes the selected data input to the output, the control input decides which data input is selected

what are common applications of a MUX?

source selection control, share one communication line between multiple senders, parallel to serial conversion

what is MUX?

multiplexer, a digital switch that has multiple inputs and a single output

what is DEMUX?

demultiplexer, a digital switch that has a single input and multiple outputs

what are common applications of a DEMUX?

share one communication line between multiple senders, serial to parallel conversion, a control for multiple lights

what is an encoder?

a circuit that produces a binary input code depending on which of he inputsare activated

what is a decoder?

a circuit that maps an n-bit code to 2^n one-hot outputs

what is 8421 BCD code?

the most commonly used binary coded decimal format, represents each decimal digit (0-9) using 4 binary bits

what is an encoder’s relation to BCD?

encoder encodes BCD

what is a decoder’s relation to BCD?

used when reading or displaying BCD values

what is an encoder’s role in BCD?

converts decimal inputs (0-9) into 4-bit BCD code

what is a decoder’s role in BCD?

converts 4-bit BCD input into one of 10 outputs (often driving display segments or indicators)

how many inputs and outputs does a decoder have?

n inputs, 2^n outputs

how many inputs and outputs does an encoder have?

2^n inputs, n outputs

what is a sequential circuit?

a circuit where output is determined by inputs and previous outputs

what does it mean for a basic latch to have asynchronous behaviour?

changes it output immediately whenever the inputs change

why is a basic latch unpredictable?

input signals may change at random times, making it hard to control when the latch updates

what can be done to a basic latch to gain control?

introduce an Enable (or Gate) signal

what do the different enable signals mean for a latch?

when enable = active, the latch is transparent and follows the inputs. when enable = inactive, the latch ignores inputs and holds its previous value

what does it mean for an enable signal to be driven by a clock in a gated latch?

latch becomes a clocked (gated) latch, it only updates during the clock’s active level

what is a gated d latch?

a modified SR latch where

• D = 1, set

• D = 0, reset

where D is data or delay

why is the gated D latch introduced?

using two states (S and R) is inconvenient, if the previous state of S is unknown, we might unnecessarily Reset first

how are flipflops constructed?

from latches from along with additional clock signals

why do flipflops respond less immediately than level-sensitive latches?

since flip-flops wait for a clock edge

what is an asynchronous storage element?

responds immediately to input changes (no clock involved)

what is a synchronous storage element?

responds only when a clock signal allows it

when does an asynchronous storage element change output?

output changes as soon as S or R (or input) changes

when does synchronous storage change output?

output changes only on a specific clock edge (rising or falling)

what is a clock?

a signal that repeatedly alternates between 0 or 1 at a fixed rate

what is a clock period?

the time for one complete cycle

what is clock frequency?

1 / clock period

what is clock triggering?

the way a flip flop responds to a clock

what are the two types of clock triggering?

positive edge triggering, negative edge triggering

how does positive-edge triggering work?

responds only when clock changes from 0 to 1

how does negative-edge triggering work?

responds only when clock change from 1 to 0

what do JK type flipflops do?

combines the behaviour of SR, D, and T flip-flops into one universal device

describe the behaviour of JK type flip flops

• J = 1, K = 0 → set Q = 1

• J = 0, K = 1 → reset Q = 0

• J = 0, K = 0 → hold previous state

• J = 1, K = 1 → toggle the output

why is a JK type flipflop considered a more robust version of SR?

free from the invalid state of the SR flip flop

where is the JK type flipflop often used?

counters, control circuits, and sequential logic systems

what are D Type flipflops?

a special case of JK flip flop where J = D and K = ¬D, and D stands for data or delay

how does a D type flip flop work?

like a gated D-latch, but responds only at clock edges (edge-triggered, not level-triggered)

how are D-type flipflops internally built?

using two latches in series

what is a T Type flipflop?

t stands for toggle, the output switches (flips) between 0 and 1 on every active clock edge when T = 1

describe the behaviour of T Type flipflops.

• if T = 0, output holds previous state (no change)

• if T = 1, output toggles on each clock edge (edge-triggered, not level-triggered)

when are T Type flipflops commonly used?

binary counters, frequency dividers, digital clocks