I semester Unit 4 combinational circuits.pptx
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- Combinational circuits consist of logic gates whose outputs depend only on the present inputs. They have no memory. - A half adder is a basic combinational circuit that adds two 1-bit numbers and produces a sum and carry output. A full adder adds three 1-bit numbers. - Other common combinational circuits described in the document include half and full subtractors, magnitude comparators, encoders, decoders, multiplexers, and demultiplexers. Each has a specific function and truth table defining its input-output behavior.
I semester Unit 4 combinational circuits.pptx
- 4. 4 • Combinational circuits consists of logic gates whose outputs depends on the present inputs • They have no memory element . • It consists of input variables , logic gates & output variables . Introduction
- 6. Half adder is a combinational logic circuit which add two 1-bit data (A,B) and produces the outputs as sum (s) and carry (C) It is the basic building block for addition of two single bit numbers. This circuit has two outputs carry and sum. Definition Block Diagram Truth table Expression: Sum, S= A⊕B Carry, C= AB
- 7. Circuit Diagram Working • When A= 0, B=0 then S=0 C=0 • When A= 0, B=1 then S=1 C=0 • When A= 1, B=0 then S=1 C=0 • When A= 1, B=1 then S=0 C=1
- 8. Full adder is developed to overcome the drawback of Half Adder circuit. It is a combinational circuit which adds three 1-bit data (A, B, Cin) to produce the output as sum(s) and carry(Co). Definition Block Diagram Truth table Expression: Sum, S= (A ⊕ B) ⊕ Cin Carry, Co= A.B + Cin (A ⊕ B)
- 9. Circuit Diagram Working • When A= 0, B=0, C=0 then S=0 Co=0 • When A= 0, B=0, C=1 then S=1 Co=0 • When A= 0, B=1, C=0 then S=1 Co=0 • When A= 0, B=1, C=1 then S=0 Co=1 • When A= 1, B=0, C=0 then S=1 Co=0 • When A= 1, B=0, C=1 then S=0 Co=1 • When A= 1, B=1, C=0 then S=0 Co=1 • When A= 1, B=1, C=1 then S=1 Co=1 Sum, S= (A ⊕ B) ⊕ Cin Carry, Co= A.B + Cin (A ⊕ B)
- 10. IT IS A COBINATIONAL CIRCUIT WHICH SUBTRACTS THE INPUT DATA AND PRODUCE THE OUTPUT AS DIFFERENCE AND BORROW
- 11. Half-subtractor is a combinational circuit which is used to subtract two 1-bit data (A, B) to give the output as Difference (Diff) and a Borrow (Br) Definition Block Diagram Truth table Expression: Difference Diff= A⊕B Borrow Br= 𝑨B
- 12. Circuit Diagram Working • When A= 0, B=0 then Diff=0 Br=0 • When A= 0, B=1 then Diff=1 Br=1 • When A= 1, B=0 then Diff=1 Br=0 • When A= 1, B=1 then Diff=0 Br=0
- 13. Full subtractor is a combinational circuit which subtracts three 1-bit data (A, B, C) to produce the output as Difference (Diff) and Borrow (Br). Definition Block Diagram Truth table Expression:
- 14. Circuit Diagram Working • When A= 0, B=0, C=0 then Diff=0 Br=0 • When A= 0, B=0, C=1 then Diff=1 Br=1 • When A= 0, B=1, C=0 then Diff=1 Br=1 • When A= 0, B=1, C=1 then Diff=0 Br=1 • When A= 1, B=0, C=0 then Diff=1 Br=0 • When A= 1, B=0, C=1 then Diff=0 Br=0 • When A= 1, B=1, C=0 then Diff=0 Br=0 • When A= 1, B=1, C=1 then Diff=1 Br=1
- 15. Full Subtractor using NAND gate
- 17. Magnitude Comparator A magnitude digital Comparator is a combinational circuit that compares two digital or binary numbers in order to find out whether one binary number is equal, less than or greater than the other binary number. We logically design a circuit for which we will have two inputs one for A and other for B and have three output terminals, one for A > B condition, one for A = B condition and one for A < B condition.
- 18. 1-Bit Magnitude Comparator • A comparator used to compare two bits is called a single bit comparator. It consists of two inputs each for two single bit numbers and three outputs to generate less than, equal to and greater than between two binary numbers. • A Comparator is a combinational circuit which compares two inputs (A , B) and gives the output as either A<B or A=B or A>B • The truth table for a 1-bit comparator is given below: From the above truth table logical expressions for each output can be expressed as follows: A>B: AB' A<B: A'B A=B: A'B' + AB
- 19. A 2-bit comparator is a combinational circuit that compares two 2-bit numbers(A & B) and produce the output as either A<B or A=B or A>B. The figure shows the block diagram of a two-bit comparator which has four inputs and three outputs Definition Block Diagram The first number A is designated as A = A1A0 and the second number is designated as B = B1B0. This comparator produces three outputs as A>B, Or A = B Or A<B.
- 22. Circuit Diagram
- 23. Encoder is a combinational circuit that converts the data from understandable format to coded format. Definition Block Diagram • A binary encoder has 2n input lines and n output lines, hence it encodes the information from 2n inputs into an n-bit code. • Any 1 input line will be activated at time • Based on the number of inputs encoders are classified as 4:2, 8:3, 16:4, decimal to BCD encoder.
- 24. This type of encoder usually consists of 10 input lines (D0 to D9) and 4 output lines (Y3 , y2, y1, y0). Each input line corresponds to the each decimal digit and 4 outputs correspond to the BCD code. This encoder accepts the decoded decimal data as an input and encodes it to the BCD output which is available on the output lines Definition Block Diagram
- 25. Circuit Diagram Truth table Expression: Y3 = D8 + D9 Y2 = D4 + D5 + D6 + D7 Y1 = D2 + D3 + D6 + D7 Y0 = D1 + D3 + D5 + D7 + D9
- 26. The Priority Encoder solves the problem that only one input should be high at a time by allocating a priority level to each input. The priority encoders output corresponds to the currently active input which has the highest priority. So when an input with a higher priority is present, all other inputs with a lower priority will be ignored. Definition Truth table Here D9 has the highest priority. For example if D7 & D5 are high at a time, then this encoder will produce the output for D as 0111 because D has more priority than D
- 27. Decoder is a combinational logic circuit that converts coded input to understandable outputs provided both of these are different from one another. The name decoder means translating of coded information from one format into another Definition Block Diagram • A binary decoder is a multi-input, multi- output combinational circuit that converts a binary code of n input lines into a one out of 2n output code. • These are used when there is need to activate exactly one of 2n output based on an n-bit input value. • Based on the number of inputs & outputs decoders are classified as 2:4, 3:8, 4:16, BCD to decimal decoder. • No of outputs = (𝟐)𝑵𝒐 𝒐𝒇 𝒊𝒏𝒑𝒖𝒕𝒔
- 28. It is a combinational circuit which converts the data from binary format to decoded format. It has 2 inputs (A, B) and 4 outputs (Y3, Y2, Y1, Y0). Any one of the output will be high at a time based on the input combination Definition Block Diagram Inputs outputs A B Y3 Y2 Y1 Y0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 Truth table Working When A = 0 and B = 1, the output Y1 will be active and when A = 1 and B = 0, then the output Y2 will be active. When both the inputs are high, then the output Y3 will be high. If the enable bit is zero then all the outputs will be set to zero. This relationship between the inputs and outputs are illustrated in the truth table
- 30. In a 3-to-8 decoder, three inputs are decoded into eight outputs. It has three inputs as A, B, and C and eight output from Y0 through Y7. Based on the combinations of the three inputs, only one of the eight outputs is selected. Definition Block Diagram Truth table Working The working of 3:8 decoder is as shown in the truth table. The decoded output depends on the input combinations A, B and C. Suppose if A = B=1 and C= 0, then the output Y6 is 1 and all other outputs are zero.
- 32. The BCD-to-decimal decoder is a combinational circuit that converts each BCD code to its decimal equivalent. The decoded output depends on the input combinations A, B, C and D. Definition Truth table Working The working of BCD to decimal decoder is as shown in the truth table. The decoded output depends on the input combinations A, B, C and D. Suppose if A =0, B=1, C= 0, D=1 then the output D5 is 1 and all other outputs are zero. The working of 3:8 decoder is as shown in the truth table. BCD inputs Decimal Outputs A B C D D9 D8 D7 D6 D5 D4 D3 D2 D1 D0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 Block Diagram
- 34. Definition A BCD to 7 segment decoder is a combinational circuit which is used to convert a binary or BCD (Binary Coded Decimal) number to the corresponding decimal number (7-segment display) . Block Diagram
- 35. Circuit Diagram Truth table
- 36. Definition A 4-to-1 multiplexer consists four data input lines as D0 to D3, two select lines as S0 and S1 and a single output line Y. The select lines S1 and S2 select one of the four input lines to connect the output line. The particular input combination on select lines selects one of input (D0 through D3) to the output Block Diagram Truth Table From the above truth table, we can write the output expressions as
- 37. Circuit:
- 38. Definition A 1-to-4 De multiplexer is a combinational circuit that sends the data (D) from input to any one of 4 outputs (Y0 Y1 Y2 Y3) depending upon the 2 select lines (S1 S0). The figure shows the block diagram of a 1-to-4 Demultiplexer Block Diagram
- 39. From the above truth table, we can write the output expressions as Truth Table
- 40. Circuit: