UNIT 2nnb djdjnesisknssjksnddnbdhdnd.pptx
- 3. ADDER • The Basic operation in digital computer is binary addition. The circuit which perform the addition of binary bits are called as Adder. • The logic circuit which perform the addition of two bit is called Half adder and three bit is called Full adder. Rules for two bit addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10
- 4. Half Adder • The two inputs of the half adders are augend and addend, the outputs are sum and carry.
- 5. Full Adder • The three inputs of the full adders are augend , addend and the carry input from the previous addition, the outputs are sum and carry. Block diagram of Full adder:
- 7. FULL ADDER
- 8. SUBTRACTOR • Subtractor is the logic circuit which is used to subtract two binary number (digit) and provides Difference and Borrow as a output. Rules for two bit subtraction 0 - 0 = 0 0 - 1 = 1 with borrow 1 1 - 0 = 1 1 - 1 = 0
- 9. HALF SUBTRACTOR • Half Subtractor is used for subtracting one single bit binary digit from another single bit binary digit.
- 10. Full Subtractor • A logic Circuit Which is used for Subtracting Three Single bit Binary digit is known as Full Subtractor. • The inputs are A,B, Bin and the outputs are D and Bout
- 12. Design of Full Subtractor using 2-Half Subtractors
- 15. MULTIPLEXER • A multiplexer is a combinational circuit that has many data inputs and a single output, depending on control or select inputs. • For N input lines, log2(N) selection lines are required, or equivalently, for 2powern input lines, n selection lines are needed. • Multiplexers are also known as “N-to-1 selectors,” parallel- to-serial converters, many-to-one circuits, and universal logic circuits. • They are mainly used to increase the amount of data that can be sent over a network within a certain amount of time and bandwidth .
- 16. 2×1 Multiplexer The 2×1 is a fundamental circuit which is also known 2- to-1 multiplexer that are used to choose one signal from two inputs and transmits it to the output.
- 18. DEMULTIPLEXER • Demultiplexer is a data distributor which takes a single input and gives several outputs. • In demultiplexer we have 1 input and 2n output lines where n is the selection line.
- 20. To implement 16 : 1 MUX using 4 : 1 MUX Using the above formula, we can obtain the same. 16 / 4 = 4 4 / 4 = 1 (till we obtain 1 count of MUX) Hence, total number of 4 : 1 MUX are required to implement 16 : 1 MUX = 4 + 1 = 5
- 21. f ( A, B, C) = m ( 1, 2, 3, 5, 6 ) with don’t care (7)using A and B as the select ∑ lines for 4 : 1 MUX, AB as select: Expanding the minterms to its boolean form and will see its 0 or 1 value in Cth place so that they can be placed in that manner.
- 22. F (P, Q, R, S) = m (0, 1, 3, 4, 8, 9, 15) ∑ Implement the following Boolean function using 8:1 multiplexer. Implementation Table
- 23. DIFFERENCE
- 24. DECODER
- 30. Implement 4:16 line decoder using 3:8 decoder
- 39. CODE CODE CONVERSION • Converting a code from one form to another is called code conversion. Hence, code conversion is a method that helps us to transform the information from one code format to another. • Code conversion is an essential process in computing and digital electronics. In digital electronics, the information is represented as letters, digits, and symbols. A group of these letters, digits, and symbols representing a piece of certain information is called a code. There are several types of codes widely used in digital electronics. Some examples of these codes are binary codes, BCD codes, Excess-3 codes, gray codes, etc.
- 40. GRAY CODE In,which any two numbers in sequence differ only by one bit change. This code is used in K-map reduction technique. The advantage is that when numbers are changing frequently, the logic gates are turning ON and OFF frequently and so are the transistors switching which characterizes power consumption of the circuit; since only one bit is changing from number to number, switching is reduced and hence is the power consumption.
- 41. Looking at gray-code (G3G2G1G0), we find that any two subsequent numbers differ in only one bit-change. The same table is used as truth-table for designing a logic circuitry that converts a given 4- bit natural binary number into gray number. For this circuit, B3 B2 B1 B0 are inputs while G3 G2 G1 G0 are outputs.
- 48. Converting BCD(8421) to Excess-3 A BCD digit can be converted to its corresponding Excess-3 code by simply adding 3 to it. Since we have only 10 digits(0 to 9) in decimal, we don’t care about the rest and marked them with a cross( X ).