UNIT I
Number System and Binary Codes: Decimal, Binary, Octal,Hexadecimal – Binary addition, Multiplication, Division–Floating point representation, Complements, BCD,Excess3, Gray Code. Arithmetic Circuits: Half adder, Full adder, Parallel binary adder, BCD adder, Half subtractor, Full subtractor, Parallel binary subtractor-Digital Logic: the Basic Gates–
NOR, NAND, XOR Gates.
PART A
1.The devices that provide the means for a computer to communicate with the user or other computers are referred to as:
(1) CPU (2) ALU (3) I/O
2 / What is the result when a decimal 5238 is converted to base 16
(1) 327.375 (2) 1476 (3) 12166
3 / Convert the decimal number 151.75 to binary.
(1) 10010111.11 (2) 10000111.11 (3) 11010011.01
4 / Base 10 refers to which number system?
(1) decimal (2) Binary (3) Hexa
5 / The number of bits used to store a BCD digit is:
(1) 1 (2) 8 (3) 4
6 / Adding the two's complement of –11 + (–2) will yield which two's complement answer?
(1) 1110 1101 (2) 1111 1001 (3) 1111 0011
7 / What are the two types of basic adder circuits?
(1) half adder and full adder (2) half adder and parallel adder (3) asynchronous and synchronous
8 / When 1100010 is divided by 0101, what will be the decimal remainder?
(1) 2 (2) 3 (3) 4
9 / The brain of any computer system is
(1) ALU (2) Memory (3) CPU
10 / Which of the following languages is more suited to a structured program?
(1) FORTRAN (2) PASCAL (3) BASIC
11 / VGA is
(1) Video Graphics Array (2) Visual Graphics Array (3) Volatile Graphics Array
12 / ALU is
(1) Arithmetic Logic Unit (2) Array Logic Unit (3) Application Logic Unit
13 / Binary equivalent of decimal number 25 is
(1) 011101 (2) 011111 (3) 011001
14 / Excess 32 (or excess with 6 bits) representation of - 15 is?
(1) 001111 (2) 010001 (3) 111111
15 / - 15 in 2's complement notation (using 6 bits)
(1) 110001 (2) 001111 (3) 010001
16 / Convert the floating point 10.001 in binary into itsequivalent decimal notation.
(1) 2.125 (2) 2.25 (3) 0.125
17 / What is the bit string represented by the Hexadecimal notation: 2D
(1) 00101100 (2) 00101101 (3) 01001101
18 / What is the output of an XOR gate with inputs 0 and 1?
(1) 0 (2) 10 (3) 1
19 / How many bytes is 5 Kbytes (kilo bytes) equivalent to?
(1) 5000 bytes (2) 5120 bytes (3) 51200 bytes
20 / Convert 65 from octal to binary
(1) 110 101 (2) 001 101 (3) 111 111
21 / Convert 0010 1110 1101 0111 from base 2 to hexadecimal
(1) 2ed7 (2) 3554 (3) 1222e
22 / Convert 111 010 110 from binary to base 8
(1) 726 (2) 28 (3) 1258
23 / Convert 1010 0101 0100 1101 from base 2 to hexadecimal
(1) a54d (2) j785 (3) 0
24 / Convert 473e from hexadecimal to base 2
(1) 0100 0111 0011 1110 (2) 0001 1000 1010 1110 (3) 1010 1011 1101 1111
25 / Base of Hexa Decimal is
(1) 8 (2) 16 (3) d
PART B
1. Write short notes on: Grey code
Gray Code
It is the non-weighted code and it is not arithmetic codes. That means there are no specific weights assigned to the bit position. It has a very special feature that, only one bit will change each time the decimal number is incremented as shown in fig. As only one bit changes at a time, the gray code is called as a unit distance code. The gray code is a cyclic code. Gray code cannot be used for arithmetic operation.
Application of Gray code
· Gray code is popularly used in the shaft position encoders.
· A shaft position encoder produces a code word which represents the angular position of the shaft.
2. Explain BCD and excess 3 codes with example.
Binary Coded Decimal (BCD) code
In this code each decimal digit is represented by a 4-bit binary number. BCD is a way to express each of the decimal digits with a binary code. In the BCD, with four bits we can represent sixteen numbers (0000 to 1111). But in BCD code only first ten of these are used (0000 to 1001). The remaining six code combinations i.e. 1010 to 1111 are invalid in BCD.
Advantages of BCD Codes
· It is very similar to decimal system.
· We need to remember binary equivalent of decimal numbers 0 to 9 only.
Disadvantages of BCD Codes
· The addition and subtraction of BCD have different rules.
· The BCD arithmetic is little more complicated.
· BCD needs more number of bits than binary to represent the decimal number. So BCD is less efficient than binary.
Excess-3 code
· The Excess-3 code is also called as XS-3 code. It is non-weighted code used to express decimal numbers. The Excess-3 code words are derived from the 8421 BCD code words adding (0011)2 or (3)10 to each code word in 8421. The excess-3 codes are obtained as follows −
·
· Example
3. Find the hexadecimal equivalent of following binary numbers
a.10110101
b.0110101110001100
a.Divide into groups of 4 digits 1011 0101
Convert each group to hex digit B 5
B5
16
b. Divide into groups of 4 digits 0110 1011 1000 1100
Convert each group to hex digit 6 B 8 C
6B8C
16
4. Convert (11101)2 to BCD.
Steps
· Step 1 -- Convert the binary number to decimal.
· Step 2 -- Convert decimal number to BCD.
· Step 1 − Convert to Decimal
· Binary Number − 111012
· Calculating Decimal Equivalent −
Step / Binary Number / Decimal NumberStep 1 / 111012 / ((1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10
Step 2 / 111012 / (16 + 8 + 4 + 0 + 1)10
Step 3 / 111012 / 2910
· Binary Number − 111012 = Decimal Number − 2910
· Step 2 − Convert to BCD
· Decimal Number − 2910
· Calculating BCD Equivalent. Convert each digit into groups of four binary digits equivalent.
Step / Decimal Number / ConversionStep 1 / 2910 / 00102 10012
Step 2 / 2910 / 00101001BCD
· Result
· (11101)2 = (00101001)BCD
5.Expalin half adder with logic circuit and truth table
Half adder is a combinational logic circuit with two inputs and two outputs. The half adder circuit is designed to add two single bit binary number A and B. It is the basic building block for addition of two single bit numbers. This circuit has two outputs carry and sum.
Block diagram
Truth Table
Circuit Diagram
PART C
1.Draw the circuit of full adder and explain its working
Full Adder
Full adder is developed to overcome the drawback of Half Adder circuit. It can add two one-bit numbers A and B, and carry c. The full adder is a three input and two output combinational circuit.
Block diagram
Truth Table
Circuit Diagram
2. Discuss all types of logic gates with symbol truth table and logic rule.
Logic gates are the basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output. The relationship between the input and the output is based on a certain logic. Based on this, logic gates are named as AND gate, OR gate, NOT gate etc.
AND Gate
A circuit which performs an AND operation is shown in figure. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
OR Gate
A circuit which performs an OR operation is shown in figure. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
NOT Gate
NOT gate is also known as Inverter. It has one input A and one output Y.
Logic diagram
Truth Table
NAND Gate
A NOT-AND operation is known as NAND operation. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
NOR Gate
A NOT-OR operation is known as NOR operation. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
XOR Gate
XOR or Ex-OR gate is a special type of gate. It can be used in the half adder, full adder and subtractor. The exclusive-OR gate is abbreviated as EX-OR gate or sometime as X-OR gate. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
XNOR Gate
XNOR gate is a special type of gate. It can be used in the half adder, full adder and subtractor. The exclusive-NOR gate is abbreviated as EX-NOR gate or sometime as X-NOR gate. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
3. Explain half and full subtractor with logic circuit and truth table.
Half Subtractors
Half subtractor is a combination circuit with two inputs and two outputs (difference and borrow). It produces the difference between the two binary bits at the input and also produces an output (Borrow) to indicate if a 1 has been borrowed. In the subtraction (A-B), A is called as Minuend bit and B is called as Subtrahend bit.
Truth Table
Circuit Diagram
Full Subtractors
The disadvantage of a half subtractor is overcome by full subtractor. The full subtractor is a combinational circuit with three inputs A,B,C and two output D and C'. A is the 'minuend', B is 'subtrahend', C is the 'borrow' produced by the previous stage, D is the difference output and C' is the borrow output.
Truth Table
Circuit Diagram
UNIT II
Combinational Logic Circuits: Boolean algebra – Karnaugh map –
Canonical form 1–Construction and properties–Implicants–Don‘t care combinations-Product of sum, Sum of products, simplifications. Sequential circuits: Flip-Flops: RS, D,JK, and T-Multiplexers–Demultiplexers–Decoder Encoder–shift registers-Counters.
PART A
1 / It is a simple combinational digital circuit built from logic gates(1) Full Adder (2) Null Adder (3) Half Adder (4) None of the above
2 / 2 It is used to subtract two inputs having more than one bit
(1) Full Subtractor (2) circuit (3) Half Subtractor (4) Counter
3 / It is a circuit, which subtracts two inputs each of one bit
(1) Full Subtractor (2) Full Adder (3) Half Subtractor (4) All of the above
4 / A code converter circuit converts the code of one form to another form (1) (2) (3) (4)
(1) Encoder (2) Code Converter (3) Decoder (4) Both (B) and (C)
5 / It is the converse of decoding and contains 2n (or fewer) input lines and n output lines
(1) Subtractor (2) Decoder (3) Multiplexer (4) Encoder
6 / It directs data from input to a selected output line
(1) Demultiplexer (2) Multiplexer (3) Coder (4) Both (A) and (B)
7 / It is a very useful combinational circuit used in communication systems
(1) Parity bit Checker (2) Parity bit Generator (3) Parity bit (4) Both (A) and (B)
8 / It is a circuit, which has a number of input lines and selection lines with one output line
(1) Sequential Circuit (2) Multiplexer (3) Counter (4) All of the above
9 / It is a circuit, which can remember values for a long time or change values when required
(1) Ripple (2) Counter (3) Circuit (4) Memory Element
10 / It is a sequential circuit that cycles through a sequence of states
(1) Multiplexer (2) Demultiplexer (3) Counter (4) Ripple
11 / It is a counter where the flip-flops do not change states at exactly the same time, as they do not have a common clock pulse.
(1) Asynchronous Ripple Counter (2) Synchronous Ripple Counter (3) Counter (4) All of the above
12 / In this logic, output depends not only on the current inputs but also on the past input values. It needs some type of memory to remember the past input values
(1) Logical Circuit (2) Connected Circuit (3) Sequential Circuit (4) Parallel Circuit
13 / In a combinational circuit, each output depends entirely on the ______inputs to the circuit.
(1) Same (2) Different (3) Common (4) Immediate
14 / In ______circuit, the output depends on both the present and the past inputs.
(1) Parallel (2) Sequential (3) Combinational (4) None of the above
15 / The steps required for the analysis of combinational circuits are
(1) Label the inputs and outputs (2) Obtain the functions of intermediate points and the outputs (3) Draw the truth table (4) All of the above
16 / Circuits that are more complex can be built using the ______method.
(1) First- level (2) Digital Level (3) Block Level (4) None of the above
17 / The four common and useful MSI circuits are
(1) Decoder (2) Demultiplexer (3) Encoder (4) All of the above
18 / Decoders often come with an enable signal, so that the device is only activated when the enable E equals to ______.
(1) 2 (2) 1 (3) 3 (4) Either (A) or (B)
19 / When more than one input can be active, the priority ______must be used.
(1) Terms (2) Words (3) Encoder (4) None of the above
20 / The Boolean expression for the multiplexer can be derived by the inspection method
(1) 6X1 (2) 3X1 (3) 5X1 (4) 4X1
21 / ______multiplexers can be constructed from smaller ones
(1) Small (2) Larger (3) Demultiplexers (4) All of the above
22 / There are______basic types of flip-flop based on clock trigger.
(1) 2 (2) 6 (3) 8 (4) 4
23 / The characteristic equation of any flip-flop describes the ______of the next state in terms of the present state and inputs. (1) (2) (3) (4)
(1) Impact (2) Behavior (3) Path (4) None of the above
24 / The normal data inputs to a flip-flop (D, S and R, J and K, T) are referred to as ______inputs
(1) Sequential (2) Asynchronous (3) Synchronous (4) Both (A) and (B)
25 / Which table indicates the input conditions of the flip-flops necessary to cause all possible next state transitions of a flip-flop?
(1) T characteristic (2) Truth (3) Flip- flop excitation (4) Excitation
PART B