Engr354: Digital Logic Circuits


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1 gr354: Digital Logic Circuits Chapter 6: Combinational Blocks Dr Curtis Nelson Chapter 6 Overview In this chapter you will learn about: Commonly used combinational subcircuits; Multipleers, which can be used or selection o signals and or implementation o general logic unctions; Circuits or encoding, decoding, and codeconversion purposes. gr354 Chapter 6
2 Combinational Circuits Combinational circuits are those whose outputs are completely deined by the inputs, i.e. no memory is involved. Eamples include Basic gates like Nands, Nors and Inverters; Multipleers, demultipleers; Decoders, encoders, code converters; Arithmetic circuits; Magnitude comparators; Parity checkers; Etc. Multipleers Devices that select one o many inputs to be routed to one output based on the binary value o select lines able used to enable or disable the complete unction; Select used to select which one o the inputs gets routed to the output. 2 n inputs i i n y output able select n select lines gr354 Chapter 6 2
3 2to Multipleer s s w w w w (a) Graphical symbol (b) Truth table w s w (c) Sumoproducts circuit 4to Multipleer s s s s w w w w (a) Graphical symbol (b) Truth table s s w w (c) Circuit gr354 Chapter 6 3
4 Using 2to Mu s to Build a 4to Mu s s w w Practical Application s 2 y (a) A 22 crossbar switch y s 2 (b) Implementation using multipleers gr354 Chapter 6 4
5 Multipleer Data Sheet 74HC53 Dual 4Line to Line Data Selectors/Multipleers Synthesis o Logic Functions Using Mu s Mu s can be used to synthesize logic unctions as ollows Create truth table; Compress as necessary; Implement. In general, an N variable unction can be implemented with one N multipleer and at most, one inverter. gr354 Chapter 6 5
6 Eample 2Input Function w w (a) Implementation using a 4to multipleer w w w (b) Modiied truth table (c) Circuit Eample 3Input Majority Function w w (b) Circuit (a) Modiied truth table gr354 Chapter 6 6
7 Eample 3Input Majority Function w w + w w 2 (b) Circuit (a) Truth table Eample 3Input XOR Function w w (b) Circuit (a) Truth table gr354 Chapter 6 7
8 DeMultipleers A demultipleer is a circuit which places the value o a single data input onto one o a number o outputs. w y w y Data An nto2 n Decoder A decoder is a device that activates one output, whose outputs are usually active low, based on the binary value o the inputs; A decoder is a minterm generator; able used to enable or disable the complete decoder unction. n inputs w w n y 2 n outputs able n gr354 Chapter 6 8
9 A 2to4 Decoder w w y y (a) Truth table w y w y w y w y (b) Graphic symbol (c) Logic circuit 3to8 Decoder Using 2to4 Decoders w y w y w w y y w y w y y 4 y 5 y 6 y 7 gr354 Chapter 6 9
10 Decoder Tree w w y y w w y y w y w y w w y w y y w y y 4 y 5 y 6 y 7 y 8 y 9 y y w y w y y 4 y 5 Decoder Data Sheet 74HC38 Single 3Line to 8Line Decoders/Demultipleers gr354 Chapter 6
11 Combinational Design with Decoders Implement the unction (a,b,c) = Sm(,3,4,5) using a decoder and random logic. Implement the unction (a,b,c) = P M(,,4,6) using a decoder and random logic. Combinational Design with Decoders and Mu s Design a digital circuit which has a 4bit input, A(H) = A 3 A 2 A A and a single output Z(H). Z(H) is high i A(H) is eactly divisible b and A(H) is not equal to 2. Note that is not divisible b in this circuit. Use a 2 to 4 decoder, a 4 to MUX, and minimum logic gates, i necessary. Note that all inputs and outputs o the MUX and decoder are asserted HIGH. gr354 Chapter 6
12 A 2 n ton Binary coder An encoder is a device that outputs a binary code representing which one o many inputs is active. The outputs are usually active low. Priority encoder assigns priority to certain inputs Used in embedded computer systems to service interrupts. w 2 n inputs n y y n n outputs A 4to2 Binary coder w w y y (a) Truth table w w y y (b) Circuit gr354 Chapter 6 2
13 gr354 Chapter 6 3 d w y d y z w Truth Table or a 4to2 Priority coder Create a circuit using the ollowing truth table or a 4to2 priority encoder (z is an output that is asserted whenever any output is asserted). w a b w c d e g (c) Truth table c e (a) Code converter w a w b c d e g a g b d (b) 7segment display BCD to 7segment Code Converter
14 A Fourbit Magnitude Comparator a 3 b 3 i 3 a 2 b 2 a b i 2 i AeqB a b i AltB AgtB Arithmetic Logic Units (74HC38 ALU) gr354 Chapter 6 4
15 Summary In this chapter you learned about: Commonly used combinational subcircuits; Multipleers, which can be used or selection o signals and or implementation o general logic unctions; Circuits or encoding, decoding, and codeconversion purposes. gr354 Chapter 6 5
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