Flip Flops

• In the electronics world, a flip-flop is a type of circuit that contains two states and are often used to store state information. By sending a signal to the flip-flop, the state can be changed. In sequential logic, it is the basic element of storage. Flip-flops are used in a number of electronics, including computers and communications equipment.

http://www.computerhope.com/jargon/f/flipflop.htm

• In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information. 

The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are a fundamental building block of digital electronics systems used in computers, communications, and many other types of systems.

http://en.wikipedia.org/wiki/Flip-flop_(electronics)#Flip-flop_types

• Flip-flops are heavily used for digital data storage and transfer and are commonly used in banks called "registers" for the storage of binary numerical data.

http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/flipflop.html

Flip Flops basics:
•Storage elements for synchronous circuits (what is synchronous?)
•Typical configurations:
•SR (set_reset)
•D
•JK
•T (toggle)
http://www.engr.uky.edu/~elias/lectures/ln_13.pdf

What is the difference between a PAL and a PLA?

PLA is programmable logic array while PAL is Programmable Array Logic.

PLA is a kind of programmable logic device used to implement combinational logic circuit.
It has Programmable AND Gate linked with Programmable OR Gate.

PAL is an combinational PLD that was developed to overcome certain disadvantage of PLA.
PLA shows longer delay due to additional fusible links which results from using two programmable array and increase circuit complexity.
Thus, PAL is used which is less complex and fast to implement. PAL consists of programmable AND linked with fixed OR.
http://wiki.answers.com/Q/What_is_the_difference_between_a_PAL_and_a_PLA

CMOS vs TTL

• What are the Basic Differences Between CMOS and TTL Signals?

CMOS compared to TTL:

CMOS components are typically more expensive that TTL equivalents.
However, CMOS technology is usually less expensive on a system level due to CMOS chips being smaller and requiring less regulation.

CMOS circuits do not draw as much power as TTL circuits while at rest.
However, CMOS power consumption increases faster with higher clock speeds than TTL does.  Lower current draw requires less power supply distribution, therefore causing a simpler and cheaper design.

Due to longer rise and fall times, the transmission of digital signals become simpler and less expensive with CMOS chips.

CMOS components are more susceptible to damage from electrostatic discharge than TTL compenents.

http://digital.ni.com/public.nsf/allkb/2D038D3AE1C35011862565A8005C5C63

microprocessors

• DRAM

Dynamic random-access memory (DRAM) is a type of random-access memory that stores each bit of data in a separate capacitor within an integrated circuit.
http://en.wikipedia.org/wiki/DRAM

• SDRAM

Synchronous dynamic random access memory (SDRAM) is dynamic random access memory (DRAM) that is synchronized with the system bus. Classic DRAM has an asynchronous interface, which means that it responds as quickly as possible to changes in control inputs.
SDRAM has a synchronous interface, meaning that it waits for a clock signal before responding to control inputs and is therefore synchronized with the computer's system bus
http://en.wikipedia.org/wiki/SDRAM

• SRAM

Static random-access memory (SRAM) is a type of semiconductor memory that uses bistable latching circuitry to store each bit.
The term static differentiates it from dynamic RAM (DRAM) which must be periodically refreshed.
SRAM exhibits data remanence, but it is still volatile in the conventional sense that data is eventually lost when the memory is not powered.

• Data remanence

Data remanence is the residual representation of data that remains even after attempts have been made to remove or erase the data. This residue may result from data being left intact by a nominal file deletion operation, by reformatting of storage media that does not remove data previously written to the media, or through physical properties of the storage medium that allow previously written data to be recovered
http://en.wikipedia.org/wiki/Data_remanence

• Transistor–transistor logic

Transistor–transistor logic (TTL) is a class of digital circuits built from bipolar junction transistors (BJT) and resistors. It is called transistor–transistor logic because both the logic gating function (e.g., AND) and the amplifying function are performed by transistors
http://en.wikipedia.org/wiki/Transistor-transistor_logic

How to Convert from Decimal to Binary

• How to Convert from Decimal to Binary

The decimal (base ten) numeral system has ten possible values (0,1,2,3,4,5,6,7,8, or 9) for each place-value. In contrast, the binary (base two) numeral system has two possible values, often represented as 0 or 1, for each place-value.

http://www.wikihow.com/Convert-from-Decimal-to-Binary

• Converting Decimal Fractions to Binary

In fact, there is a simple, step-by-step method for computing the binary expansion on the right-hand side of the point. We will illustrate the method by converting the decimal value .625 to a binary representation..

Step 1: Begin with the decimal fraction and multiply by 2. The whole number part of the result is the first binary digit to the right of the point.

Because .625 x 2 = 1.25, the first binary digit to the right of the point is a 1.
So far, we have .625 = .1??? . . . (base 2) .

Step 2: Next we disregard the whole number part of the previous result (the 1 in this case) and multiply by 2 once again. The whole number part of this new result is the second binary digit to the right of the point. We will continue this process until we get a zero as our decimal part or until we recognize an infinite repeating pattern.

Because .25 x 2 = 0.50, the second binary digit to the right of the point is a 0.
So far, we have .625 = .10?? . . . (base 2) .

Step 3: Disregarding the whole number part of the previous result (this result was .50 so there actually is no whole number part to disregard in this case), we multiply by 2 once again. The whole number part of the result is now the next binary digit to the right of the point.

Because .50 x 2 = 1.00, the third binary digit to the right of the point is a 1.
So now we have .625 = .101?? . . . (base 2) .

Step 4: In fact, we do not need a Step 4. We are finished in Step 3, because we had 0 as the fractional part of our result there.

Hence the representation of .625 = .101 (base 2) .

You should double-check our result by expanding the binary representation.

• Infinite Binary Fractions

the binary representation of the decimal fraction 1/10 is, in fact, infinite.Step 1: Begin with the decimal fraction and multiply by 2. The whole number part of the result is the first binary digit to the right of the point.

Because .1 x 2 = 0.2, the first binary digit to the right of the point is a 0.
So far, we have .1 (decimal) = .0??? . . . (base 2) .

Step 2: Next we disregard the whole number part of the previous result (0 in this case) and multiply by 2 once again. The whole number part of this new result is the second binary digit to the right of the point. We will continue this process until we get a zero as our decimal part or until we recognize an infinite repeating pattern.

Because .2 x 2 = 0.4, the second binary digit to the right of the point is also a 0.
So far, we have .1 (decimal) = .00?? . . . (base 2) .

Step 3: Disregarding the whole number part of the previous result (again a 0), we multiply by 2 once again. The whole number part of the result is now the next binary digit to the right of the point.

Because .4 x 2 = 0.8, the third binary digit to the right of the point is also a 0.
So now we have .1 (decimal) = .000?? . . . (base 2) .

Step 4: We multiply by 2 once again, disregarding the whole number part of the previous result (again a 0 in this case).

Because .8 x 2 = 1.6, the fourth binary digit to the right of the point is a 1.
So now we have .1 (decimal) = .0001?? . . . (base 2) .

Step 5: We multiply by 2 once again, disregarding the whole number part of the previous result (a 1 in this case).

Because .6 x 2 = 1.2, the fifth binary digit to the right of the point is a 1.
So now we have .1 (decimal) = .00011?? . . . (base 2) .

Step 6: We multiply by 2 once again, disregarding the whole number part of the previous result. Let's make an important observation here. Notice that this next step to be performed (multiply 2. x 2) is exactly the same action we had in step 2. We are then bound to repeat steps 2-5, then return to Step 2 again indefinitely. In other words, we will never get a 0 as the decimal fraction part of our result. Instead we will just cycle through steps 2-5 forever. This means we will obtain the sequence of digits generated in steps 2-5, namely 0011, over and over. Hence, the final binary representation will be.

.1 (decimal) = .00011001100110011 . . . (base 2) .
The repeating pattern is more obvious if we highlight it in color as below:

.1 (decimal) = .00011001100110011 . . . (base 2) .

http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.htm

• We can construct binary fractions using a binary "point", in the same was as we do with decimal:

101.101
||| |||
||| ||2-3 (1/8)
||| |2-2  (1/4)
||| 2-1   (1/2)
||20     (1)
|21       (2)
        22        (4)
And so the above number represents 4 + 1 + 1/2 + 1/8 = 5 5/8 (5.625)

http://turing.cs.camosun.bc.ca/COMP166/resources/floatingpoint.html

• Binary Numbering

0.101

= 0 X 20 + 1 X 2-1 + 0 X 2-2 + 1 X 2-3

= 0 + 1/2 + 0 + 1/8

= 4/8 + 1/8

= 5/8


http://cs.furman.edu/digitaldomain/more/binary/bin1.html

• 1. Which of the following is the binary representation of 4 5/8?

A. 100.11

ANSWER: D


https://docs.google.com/viewer?a=v&q=cache:00oarkgsJgkJ:site.iugaza.edu.ps/lalsaedi/files/2010/02/Chapter_One.doc+&hl=tr&pid=bl&srcid=ADGEESjzXurOtyhphMb3gIqn3eIZoYb-rzzeM8VZfuwgjEkeUT3qz6Owdai6A5spFoV9glErHyRAj6EarlH-34TTNh2pLRWHfuR1FFwSmZMgIaTCnS1Frc-dZb873BWlEwdPq7zcNzVB&sig=AHIEtbRxYL1hEMxqJSLu9JaEE3mZTjp23w

• Example: Convert decimal 44 to binary.

DIVIDE
44 / 2 = 22 remainder = 0
22 / 2 = 11 remainder = 0
11 / 2 =  5 remainder = 1
 5 / 2 =  2 remainder = 1
 2 / 2 =  1 remainder = 0
 1 / 2 =  0 remainder = 1


REVERSE THE ORDER OF REMAINDERS
The bits, in the order they were generated is 001101 Reversing the order of bits we get 101100. Properly padded with leading zeroes to fill out one byte, we get 01011000

http://www.inetdaemon.com/tutorials/basic_concepts/number_systems/binary/conversion.shtml

• Example.  Convert the decimal number 29410 into its binary number equivalent.

Number 294 Dividing each number by "2" gives a result plus a remainder. The binary result is obtained by placing the remainders in order with the least significant bit (LSB) being at the top and the most significant bit (MSB) being at the bottom.
divide by 2
result 147 remainder 0  (LSB)
divide by 2
result 73 remainder 1
divide by 2
result 36 remainder 1
divide by 2
result 18 remainder 0
divide by 2
result 9 remainder 0
divide by 2
result 4 remainder 1
divide by 2
result 2 remainder 0
divide by 2
result 1 remainder 0
divide by 2
result 0 remainder 1  (MSB)

Then, the decimal to binary conversion gives the decimal number 29410 equivalent of 1001001102 in binary, reading from right to left.

http://www.electronics-tutorials.ws/binary/bin_2.html

Binary-coded decimal(BCD)

• Binary-coded decimal

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight, although other sizes (such as six bits) have been used historically

As an example, encoding the decimal number 91 using uncompressed BCD results in the following binary pattern of two bytes:
Decimal:          9          1
Binary :  0000 1001  0000 0001

In packed BCD, the same number would fit into a single byte:
Decimal:     9    1
Binary :  1001 0001
https://en.wikipedia.org/wiki/Binary-coded_decimal

• BCD to deciman conversion

Short for Binary Coded Decimal, BCD is also known as packet decimal and is numbers 0 through 9 converted to four-digit binary. Below is a list of the decimal numbers 0 through 9 and the binary conversion.

Using this conversion, the number 25, for example, would have a BCD number of 0010 0101 or 00100101. However, in binary, 25 is represented as 11001.

http://www.computerhope.com/jargon/b/bcd.htm

Digital System Design

Digital System Design
Combinational Logic Building Blocks

Multiplexers
Called n-to-1 multiplexer

Decoders
Called n-to-2n decoder

Demultiplexers
Called 1-to-n demultiplexer

Encoders
Called 2n-to-n encoder

https://docs.google.com/viewer?a=v&q=cache:b0jai5RJPFIJ:ece.gmu.edu/coursewebpages/ECE/ECE545/F10/viewgraphs/ECE545_lecture1_digital_logic_review.ppt+&hl=en&pid=bl&srcid=ADGEESjjerAWeVXZpjaIvzRlh4Jpa1-TafvQr9CpnnN55BUVTvcvTKSYJlBgic2e_hhQlR2-SjmbQdiEgsFerWL3xYQGwdvWKJxAhZLr-KOjsIZurtH8tglVPDfnfJLvrs-7JjtgQLBi&sig=AHIEtbSu7bzXI9GzheG6Chub1-b5V0e-5w