Engistan.com [Digital Electronics for IBPS IT-Officer 2014] Digital circuit: Circuit in which the signal used can have fixed number of discrete states. It consists of logic gates, electronic devices. Mobile phone, digital watch, calculators, computers, video games etc are example of digital circuits. Advantages of digital circuits: • Less susceptible to noise or degradation in quality than analog circuits. • Easy to perform error detection and correction with digital signals. Digital logic: • It shows the communication between circuits and hardware within a computer. • It is representation of signals and sequences of a digital circuit through numbers. • Digital logic is typically embedded in most electronic devices. Digital Signal/ Logic signal: It is a physical signal which is used for representation of a sequence of discrete values. They can be represented as: • Truth values:- true (T) and false (F) • Boolean values:-1 and 0. • Voltage:- represented as “high” (H) or “low” (L) • For switch:- on/off OR open/close etc Operations on Logic Signals: A and B two signals are input set for a given circuit and produces a output signal C, which depends on A and B. C can be result of AND, OR ,NOT, NAND, NOR, XOR function between A and B. Logic gates: These are use to perform logic operations on logical inputs and produces a single logical output. If A is a digital signals then A could be either TRUE (a logical 1) or FALSE (a logical 0). • And Gate: The output of AND gate is TRUE only if both the inputs to the AND gate is TRUE. Truth table for And gate: Engistan.com | [Engineer’s Community] 1 engistan.com
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v P ] v X } u [Digital Electronics for IBPS IT-Officer 2014] Input Output A B C False False False False True False True False False True True True Symbol for And gate: Also C= A.B
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Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
Digital circuit: Circuit in which the signal used can have fixed number of discrete states. It consists of logic gates, electronic devices. Mobile phone, digital watch, calculators, computers, video games etc are example of digital circuits.
Advantages of digital circuits:
• Less susceptible to noise or degradation in quality than analog circuits. • Easy to perform error detection and correction with digital signals.
Digital logic:
• It shows the communication between circuits and hardware within a computer. • It is representation of signals and sequences of a digital circuit through numbers. • Digital logic is typically embedded in most electronic devices.
Digital Signal/ Logic signal: It is a physical signal which is used for representation of a sequence of discrete values. They can be represented as:
• Truth values:- true (T) and false (F) • Boolean values:-1 and 0. • Voltage:- represented as “high” (H) or “low” (L) • For switch:- on/off OR open/close etc
Operations on Logic Signals:
A and B two signals are input set for a given circuit and produces a output signal C, which depends on A and B.
C can be result of AND, OR ,NOT, NAND, NOR, XOR function between A and B.
Logic gates: These are use to perform logic operations on logical inputs and produces a single logical output. If A is a digital signals then A could be either TRUE (a logical 1) or FALSE (a logical 0).
• And Gate: The output of AND gate is TRUE only if both the inputs to the AND gate is TRUE. Truth table for And gate:
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
1 0 0
1 1 1
Also C= or = A’B’+ AB
Note: NOR gates alone or alternatively NAND gates alone can be used to reproduce the functions of all the other logic gates so they are called Universal gates.
Number system:
In digital logic number can be represented in various forms:
Number System Base Representation of numbers is using
Binary number 2 0 (zero) and 1 (one)
Decimal numbers 10 0 to 9
Octal numbers 8 0 to 7
Hexadecimal 16 0 to 9 digits and A to Z alphabets
Complements: They are used in digital computer for simplifying the subtraction operation and for logic manipulation.
Codes in digital logic:
Binary Codes: In such case signal will have 2 values (0/1) and circuit elements will have two stable states.
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
T11 : De Morgan's Theorem
(a)
(b)
Methods to solve Boolean expression:
Boolean algebra: area of mathematics using which Boolean expression are solved.
Karnaugh map (K map): A Karnaugh Map is a grid-like representation of a truth table. A Karnaugh map has zero and one entries at different positions. Each position in a grid corresponds to a truth table entry.
For example:
A B C V 0 0 0 0 0 0 1 0
0 1 0 0 0 1 1 1 1 0 0 0
1 0 1 1 1 1 0 1 1 1 1 1
Logic circuits are of two types:
• Combinational: It consists of logic gates whose outputs at any time are determined directly from the present input without regards to previous inputs.
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
CIRCUIT DIAGRAM
Full Substracor: This circuit consists of three binary inputs (two bits that used need to substract and one borrow) and two binary outputs (difference and borrow).
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
Binary parallel Adder: It produces arithmetic sum of 2 binary numbers in parallel. It consists of full adder connected in cascade. It work on the carry propagation concept.
BLOCK DIAGRAM
Decimal adder: It need minimum of 9 inputs in decimal form and produces 5 outputs of BCD form.
BCD Adder: used to add two BCD digits and produces a sum digit also in BCD.
Magnitude Comparator: Used to compare two numbers
Decoder: Converts binary information from n inputs to a max of 2^n unique information. For example:
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
• Relay actuator
BLOCK DIAGRAM
Demultiplexers: A decoder with enable function is demux. It receive information on a signal line transmit this information on one of 2^n possible output lines. The selection of output is controlled by bit values of n selection lines.For example:
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
• Octal to binary encoder • Hexadecimal to binary encoder
BLOCK DIAGRAM
Multiplexers: It selects binary information from one of the many input lines(max 2^n) and directs it to a single output line. It has n select lines whose combination determine which input is seleted. For example:
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
TRUTH TABLE
Sequential circuits:
Basic Flip Flop circuits: a flip-flop or latch is a circuit that has two stable states and used to store state information. It is also called bistable multivibrator. The circuit can have one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. It is constructed from 2 nand and 2 nor gates.
Type of flip flop:
Clocked RS flip flop: Basic flip flop plus clock is Clocked RS flip flop.
Engistan.com [Digital Electronics for IBPS IT-Officer 2014]
Type of ripple counter:
• binary ripple counter • BCD ripple counter
Synchronous counter: The input pulse are applied to all the clock pulse input of flip flops.
2-BIT SYNCHRONOUS UP COUNTER The JA and KA inputs of FF-A are tied to logic 1. So FF-A will work as a toggle flip-flop. The JB and KBinputs are connected to QA.
LOGICAL DIAGRAM
Type of Synchronous counter:
• Binary Synchronous counter. • Binary up down counter • BCD Counter
Classification of counters
Depending on the way in which the counting progresses, the synchronous or asynchronous counters are classified as follows:-
• Up counters • Down counters • Up/Down counters
Modulus Counter (MOD-N Counter):
The 2-bit ripple counter is called as MOD-4 counter and 3-bit ripple counter is called as MOD-8 counter. So in general, an n-bit ripple counter is called as modulo-N counter. Where,MOD number = 2^n