The Digital Logic Level

¡Supera tus tareas y exámenes ahora con Quizwiz!

If an input is 1, the position of the input is the value of output 0 and output 1 in binary rep. EX. If Input 1 = 1 then Output 1 = 0 and Output 0 = 1 If input 2 = 1 then Output 1 = 1 and Output 1 = 0

What is the technique for determining the values of the outputs in a decoder?

Add the value of A,B, and C in. The result in decimal rep should be translated to binary. The first bit is the carry out and the second is the sum. Ex. A = 1 B = 1 C in = 0 Result = 2 (Decimal) 2 (Decimal) >> 10 (Binary) Carry out = 1 Sum = 0

What is the technique to calculating a full adder.

A valid ensures that the encoding is valid. It is 1 when at least one input is 1 otherwise valid is 0.

What is the valid and when is its value 1.

Full Adder

What truth table is displayed?

Half Adder

What truth table is displayed?

NAND and NOR because any Boolean function can be computed using either or them.

What two gates are said to be complete?

Full Adder

What type of circuit is displayed?

Half Adder

What type of circuit is displayed?

Inverter

What's another name for a NOT gate?

(A = 1 AND B = 0) OR (B = 1 AND C = 0)

Compute the input values:

A = 1 and B = 0 and C = 1

Compute the input values:

Depends on the function select input line F0 and F1 (00,01,10,11)

How do we choose which operation to perform in an ALU.

Reducing the number of gates by finding other circuits that compute the same function as the original by with few gates.

How do you reduce the chip area to minimize power consumption and increase speed?

The select lines (control lines) that feed a binary number into the selector

How does an ALU choose which operation to perform?

3 because 2^n data inputs to n control outputs. So 2^3 = 8.

How many control inputs are needed for a multiplexer with 8 data inputs?

1 output

How many outputs can be assorted at a time in a decoder?

three

How many transistors do AND and OR Gates need?

two

How many transistors do NAND and NOR Gate need?

Sum = 1 Carry = 0

If A = 0 and B = 1. What is the Sum and Carry in a Half Adder.

Sum = 1 Carry out = 0

If A = 1 and B = 0 and Carry In = 0. What is the Sum and Carry out in a Full Adder?

Sum = 0 Carry out = 1

If A = 1 and B = 1 and Carry In = 0. What is the Sum and Carry out in a Full Adder?

Sum = 0 Carry = 1

If A = 1 and B = 1. What is the Sum and Carry in a Half Adder.

If the binary value of the control line is k output ___ is selected.

0 7

In a 8 In/output circuit, a left shift is made by placing a ____ into the bit ___.

1 0

In a 8 in/output circuit, a right shift is made by placing a ___ into the bit ____.

4 outputs

In a Decoder. How many output lines are made with 2 inputs.

3 A,B, and Carry In

In a Full Adder, how many inputs are given? What are the inputs?

2 Sum and Carry Out

In a Full Adder, how many outputs are given? What are the outputs?

1. If A and B are both 1 2. If A or B is 1 and the Carry in bit is also 1.

In a Full Adder, the Carry out is 1 if?

If an odd number of A,B, and the Carry in are 1.

In a Full Adder, the sum is 1 if?

Valid = 1 Output 1 = 1 Output 2 = 1

In an 4 to 2 encoder. If only Input 3 = 1 what is the value for valid, Output 1 and Output 0.

Yes, most computers use NAND and NOR. Also they are complete.

Is it true that NAND and NOR gates are simpler that AND and OR gates?

1. bar (compliment) 2. 0

Place a ____ on a variable that equals _____

True

True or False. After constructing the truth table you only focus on the columns that result in a 1 (true)

False. It is more convenient to implement a gate with a single gate type.

True or False. It is more convenient to implement a circuit using mutiple types of gates.

True

True or False. No matter what value is on the control line, all except one line is 0. And the one line may output 0 or 1 depending on the value of the selected line.

Input: A,B, Select Lines Output: C, Carry out

What are the inputs in the ALU? outputs?

1. Get input with the highest position value with a 1 2. Only 1 Input is chosen 3. Choose an Input equal to 1 4. Encode output in binary

What are the main rules to solving an encoder?

1. Make a truth table. 2. Provide an inverter to make the compliments of inputs with 0. 3. Draw an AND gate for each term with a 1 in the results column. 4. Wire the AND gates to the appropriate inputs. 5. Feed the output of all the AND gates into an OR gate.

What are the steps to constructing a circuit for any boolean function?

PGAs and LGAs (Pin Grid Arrays and Land Grid Arrays)

What are the two common packages for larger chips.

ALU

What circuit is displayed?

XOR Gate

What do these circuits construct?

Logical 1 or true or on

What does "high" (Vcc) mean?

Logical 0 or false or off

What does "low" (GND) mean?

One byte (8 bits)

What does A7:A0 indicate?

Boolean OR

What does a (+) mean?

Logical 0

What does a signal between 0 and 0.5v represent?

Logical 1

What does a signal between 1 and 1.5v represent?

Boolean AND

What does an implied multiplication or a dot mean?

Performs arithmetic & logic (boolean) operations. 1. Addition (A + B) 2. AND (A * B) 3. OR (A or B) or (A + B) 4. Not (!A)

What does the ALU do?

A(B + C)

What does this construct?

AND Gate (AB)

What does this construct?

NOT Gate (!A)

What does this construct?

OR Gate (A+B)

What does this construct?

AB (AND Gate)

What does this equal to ?

A + B (OR Gate)

What does this equal to?

Addition

What function is represented by the following binary code: 00

AND

What function is represented by the following binary code: 01

What function is represented by the following binary code: 10

NOT

What function is represented by the following binary code: 11

Absorption Law

What identity is this?

Associative Law

What identity is this?

Commutative Law

What identity is this?

DeMorgan's law (AND form) Also a NAND gate

What identity is this?

DeMorgan's law (OR form) Also a NOR gate

What identity is this?

Distributive Law

What identity is this?

Idempotent Law

What identity is this?

Identity law

What identity is this?

Inverse Law

What identity is this?

Null law

What identity is this?

A circuit that compares two input words. Ex. if equal == logical 1. if not equal == logical 0.

What is a Comparator?

A IC Package with 2 rows of pins that hold smaller chips such as micro controllers or RAM chips

What is a Dual Inline Package? (DIP)

A circuit with 2^n data inputs, one data output, and n control inputs, that selects one of the data inputs by gating the input line to the output.

What is a Multiplexer?

A circuit with multiple inputs and outputs in which outputs are uniquely determined by the current input values.

What is a combinational circuit?

A circuit that takes n bit number as an input and uses it to selects exactly one of the 2^n output lines.

What is a decoder?

A decoder decodes an n-bit binary number input to assort the corresponding 2^n bit output

What is a decoder?

The inverse of a multiplexer. Routes its single input signal to one of 2^n outputs, depending on the values of the n control lines.

What is a demultiplexer?

Arithmetic Logic Unit

What is an ALU stand for?

A rectangular piece unit made of silicon that holds gates.

What is an Integrated Circuits (IC) or chip?

An encoder encrypts a message

What is an encoder?

2-bit decoder that generate the enable signals for the 4 operations, based on the control signals F0 and F1.

What is located in the lower left-hand corner of the ALU?

The Full Adder that computes the sum.

What is located in the lower right-hand corner of the ALU?

Logic unit that computes the boolean operations (AND, OR, and NOT)

What is located in the upper left-hand corner of the ALU?

The rightmost bit

What is the least significant bit?

If the input is equal to 0 then the the inputs are grounded. If the input equals to 1 then they are wired to logical 1 or Vcc.

What is the majority function?

The leftmost bit

What is the most significant bit?

AND Gate