Quiz 3

Compare multiplexers vs. decoders

1. A multiplexer uses n binary select bits to choose from a maximum of 2^n unique input lines. 2. Multiplexers and decoders both can decode minterms. 3. Decoders have n number of output lines while multiplexers have only one output line. 4. The decoded minterms are used to select data from one of up to 2^n unique data input lines 5. The output of the multiplexer is the data input whose index is specified by the n bit code.

Register

1. An n-bit register consists of n flip flops and can store any binary information of n bits. 2. a register may also have combinational circuits associated with each flip flop. 3. The flip flops hold binary information and the combinational circuits control how and when new information is transferred to the register.

Boolean Expressions using Multiplexers

1. Construct the truth table. 2. Write a Boolean expression using the relationship between the least significant bit variable and the output. 3. Each two entries of the least significant bit are compared to the output. 4. The assignment is either be the variable its complement 1 or 0. 5. The least significant variable can then be controlled by the other variables according to the truth table. 6. Assign the variables to each corresponding switch of the multiplexer 7. The size of the multiplexer is 2^n-1 where n is the number of boolean variables.

3-to-8 line decoder

3 inputs & 8 outputs. 3 input AND gates can be used to realize each output.

What is a register?

A group of flip flops where each flip flop stores 1 bit of information. A bit-wise extension of a FF consisting of n FFs driven by a common clock signal.

Shift register

A register capable of shifting binary values in one or both directions. It consists of a chain of flip flops in cascade, with the output of one stage connected to the input of the next stage. All flip flops receive a common clock pulse.

Decoder

Accepts a binary value and decodes it to one particular output out of several outputs

What is an application of a decoder?

Converts from binary to decimal

What are the outputs of a 2-4 decoder in terms of inputs A0 and A1?

D0 = A1`A0` D1 = A1`A0 D2 = A1 A0` D3 = A1 A0

Serial transfer

Data transfer one bit at a time 1 bit per clock pulse. Data loop back for register A.

Parallel data transfer

Data transferred from register X to register Y (copying). Each bit is connected to a corresponding bit rate is 4 bits/clk

What does a multiplexer consist of?

Inputs (multiple) = 2^n Outputs (single) Selectors (# depends on # of inputs) = n Enable (active high or active low)

What is the input/outputs of a Decoder?

Inputs: n binary digits Outputs (2^n numbered from 0->2^n-1) only one is active Disable/enable (active high or active low)

2-to-4 NAND decoder

Outputs are switched so that everything is 1 except for one output that equals 0. The Decoder is enabled when E=0

Encoder

Performs the inverse operation of a decoder 2^n input lines and n output lines (decimal to binary)

What is a demultiplexer?

Performs the inverse operation of a multiplexer. Receives information from a single line and transmits it to one of 2^n possible output lines. N selection inputs select the specified output.

How do you cascade multiplexers? (i.e. using three 2-1 MUX to make one 4-1 MUX)

Separate the four inputs as two inputs being in one MUX and the other two being in the second with both of these multiplexers using the same selector, S0. Then the result of those two multiplexers become the input to the final MUX with selector S1.

How to implement boolean function with a decoder?

Since any boolean function can be expressed as a sum of minterms, one can use a decoder and external OR gates to implement any combinational function.

Combining two 2-4 decoders to form one 3-8 decoder

The highest bit is used for the enable input of each decoder, with one being passed through an inverter so that way only one decoder is enabled at one time.

If you had to implement both a decoder and a multiplexer in circuitry what would be the difference

The multiplexer has an extra OR gate. A1 and A0 are the two inputs in decoder. There are four inputs in multiplexer.

What is a priority encoder?

accepts multiple values and encodes them works when more than one input is active

Multiplexer

can use addressing bits to select one of several input bits to be the output. A selector chooses a single data input and passes it to the MUX output. It has one output selected at a time.

n-to-m line decoder

m < 2^n and generate 2^n or fewer minterms of n input variables.

How does a priority encoder work?

when more than one input is active, sets output to correspond to highest input.

How can an encoder be implemented?

with 3 OR gates