Cs 121 Ch 4 3 Combinational Logic Binary

Cs 121 Ch 4 - 3 Combinational Logic

Binary Decoder ° Black box with n input lines and 2 n output lines ° Only one output is a 1 for any given inputs Binary Decoder 2 n outputs

2 -to-4 Binary Decoder Truth Table: F 0 = X'Y' F 1 = X'Y ° From truth table, circuit for 2 x 4 decoder is: ° Note: Each output is a 2 variable minterm (X'Y', X'Y, XY' or XY) X Y 2 -to-4 Decoder F 2 = XY' F 3 = XY F 0 F 1 F 2 F 3 X Y

3 -to-8 Binary Decoder Truth Table: F 0 = x'y'z' F 1 = x'y'z F 2 = x'yz' F 3 = x'yz F 4 = xy'z' F 5 = xy'z F 6 = xyz' F 0 X Y Z F 7 = xyz F 1 3 -to-8 Decoder F 2 F 3 F 4 F 5 F 6 F 7 x y z

Decoder Expansions : Use two 3 to 8 decoders to make 4 to 16 decoder ° Enable can also be active high ° In this example, only one decoder can be active at a time. ° x, y, z effectively select output line for w Q: How to construct a 5 -to-32 decoder?

Encoders ° If the a decoder's output code has fewer bits than the input code, the device is usually called an encoder. e. g. 2 n-to-n ° The simplest encoder is a 2 n-to-n binary encoder • One of 2 n inputs = 1 • Output is an n-bit binary number 2 n inputs . . . Binary encoder . . . n outputs

8 -to-3 Binary Encoder At any one time, only one input line has a value of 1. I 0 I 1 I 2 I 3 Inputs I 0 1 0 0 0 0 I 2 0 0 1 0 0 0 I 3 0 0 0 1 0 0 I 4 0 0 1 0 0 0 Outputs I 5 0 0 0 1 0 0 I 6 0 0 0 1 0 y 2 = I 4 + I 5 + I 6 + I 7 y 1 = I 2 + I 3 + I 6 + I 7 I 4 I 5 I 6 I 7 y 0 = I 1 + I 3 + I 5 + I 7 0 0 0 0 1 y 2 0 0 1 1 y 1 0 0 1 1 y 0 0 1 0 1

8 -to-3 Priority Encoder • What if more than one input line has a value of 1? • Ignore “lower priority” inputs. • X: don't-care conditions. V: valid output indicator. Inputs I 0 0 1 X X X X I 1 0 0 1 X X X I 2 0 0 0 1 X X X I 3 0 0 1 X X I 4 0 0 0 1 X X X Outputs I 5 0 0 0 1 X X I 6 0 0 0 0 1 X I 7 0 0 0 0 1 y 2 x 0 0 1 1 y 1 x 0 0 1 1 y 0 x 0 1 0 1 V 0 1 1 1 1

Encoder Application (Monitoring Unit) ° Encoder identifies the requester and encodes the value ° Controller accepts digital inputs. Alarm Signal r o g F in d ea R Contoller Response Machine 1 Machine 2 Encoder Machine n Action Machine Code Controller

Multiplexers ° Select an input value with one or more select bits ° Use for transmitting data ° Allows for conditional transfer of data ° Sometimes called a mux

Multiplexers ° Funneling several data lines into a single one for transmission to another point r o g F in d a e R ° Data select control determines which input is transmitted 38

4– to– 1 - Line Multiplexer

Quadruple 2–to– 1 -Line Multiplexer r o g F in d a e R ° E enable bit ° S select bit ° 4 bit inputs

Typical multiplexer uses r o g F in e R d a

Summary ° Decoder allows for generation of a single binary output from an input binary code • For an n-input binary decoder there are 2 n outputs ° Decoders are widely used in storage devices (e. g. memories) ° Encoders all for data compression ° Priority encoders rank inputs and encode the highest priority input ° Multiplexers are fundamental digital components • Can be used for logic • Useful for datapaths • Scalable