# The World of 2-The Digital World, Powers of 2, From 0 to 100

A list of powers of 2, from 2^0 to 2^100. This list is Particularly useful for calculation in digital applications. Where every thing consists of 2 values i.e., 0's (Zeros) & 1's (Ones). Suppose you have 128x64 dots GLCD, here also 2's power prevail, as 128=2^7 & 64=2^6. If your Processor is 16 bits, it will support a maximum memory of 65536 bits, here 2^16=65536. So these numbers are important.
Also for programming point of view you can build lookup table of powers of 2 just by copying it! Particularly you may use it in VHDL, C/C++ or Java based applications. So just have a look at the list.

 Power Of 2 Value of 2^n (Where n=corresponding power of 2) 0 1 1 2 2 4 3 8 4 16 5 32 6 64 7 128 8 256 9 512 10 1,024 11 2,048 12 4,096 13 8,192 14 16,384 15 32,768 16 65,536 17 131,072 18 262,144 19 524,288 20 1,048,576 21 2,097,152 22 4,194,304 23 8,388,608 24 16,777,216 25 33,554,432 26 67,108,864 27 134,217,728 28 268,435,456 29 536,870,912 30 1,073,741,824 31 2,147,483,648 32 4,294,967,296 33 8,589,934,592 34 17,179,869,184 35 34,359,738,368 36 68,719,476,736 37 137,438,953,472 38 274,877,906,944 39 549,755,813,888 40 1,099,511,627,776 41 2,199,023,255,552 42 4,398,046,511,104 43 8,796,093,022,208 44 17,592,186,044,416 45 35,184,372,088,832 46 70,368,744,177,664 47 140,737,488,355,328 48 281,474,976,710,656 49 562,949,953,421,312 50 1,125,899,906,842,624 51 2,251,799,813,685,248 52 4,503,599,627,370,496 53 9,007,199,254,740,992 54 18,014,398,509,481,984 55 36,028,797,018,963,968 56 72,057,594,037,927,936 57 144,115,188,075,855,872 58 288,230,376,151,711,744 59 576,460,752,303,432,488 60 1,152,921,504,606,846,976 61 2,305,843,009,213,693,952 62 4,611,686,018,427,387,904 63 9,223,372,036,854,775,808 64 18,446,744,073,709,551,616 65 36,893,488,147,419,103,232 66 73,786,976,294,838,206,464 67 147,573,952,589,676,412,928 68 295,147,905,179,352,825,856 69 590,295,810,358,705,651,712 70 1,180,591,620,717,411,303,424 71 2,361,183,241,434,822,606,848 72 4,722,366,482,869,645,213,696 73 9,444,732,965,739,290,427,392 74 18,889,465,931,478,580,854,784 75 37,778,931,862,957,161,709,568 76 75,557,863,725,914,323,419,136 77 151,115,727,451,828,646,838,272 78 302,231,454,903,657,293,676,544 79 604,462,909,807,314,587,353,088 80 1,208,925,819,614,629,174,706,176 81 2,417,851,639,229,258,349,412,352 82 4,835,703,278,458,516,698,824,704 83 9,671,406,556,917,033,397,649,408 84 19,342,813,113,834,066,795,298,816 85 38,685,626,227,668,133,590,597,632 86 77,371,252,455,336,267,181,195,264 87 154,742,504,910,672,534,362,390,528 88 309,485,009,821,345,068,724,781,056 89 618,970,019,642,690,137,449,562,112 90 1,237,940,039,285,380,274,899,124,224 91 2,475,880,078,570,760,549,798,248,448 92 4,951,760,157,141,521,099,596,496,896 93 9,903,520,314,283,042,199,192,993,792 94 19,807,040,628,566,084,398,385,987,584 95 39,614,081,257,132,168,796,771,975,168 96 79,228,162,514,264,337,593,543,950,336 97 158,456,325,028,528,675,187,087,900,672 98 316,912,650,057,057,350,374,175,801,344 99 633,825,300,114,114,700,748,351,602,688 100 1,267,650,600,228,229,401,496,703,205,376

# Zigbee(IEEE 802.15.4)- Working & Comparision With Other Wireless Standards

 Zigbee Module
Introduction:
ZigBee is the most popular industry wireless mesh networking standard for connecting sensors, instrumentation & control systems. ZigBee provides several benefits just because it is an industry standard supported by multiple solution providers. ZigBee solutions are relatively inexpensive because several suppliers have already implemented ZigBee-based ICs & modules in anticipation of high volumes for a standard solution. ZigBee-based solutions also offer users independence from any one supplier because one company’s ZigBee networking solution can be substituted for another’s. ZigBee also offers the potential for interoperability among different suppliers’ products. In theory, a ZigBee application deployed in a location can use other existing ZigBee nodes in that location to extend its range and improve its communication reliability.
ZigBee delivers solid wireless connectivity for sensors and actuators in applications that can need the general benefits of mesh networking (i.e., coverage and reliability) at a reasonable price, power consumption, node-to-node range, and master-oriented operation. ZigBee is actually uses OSI Model layer, & is designed to operate over a radio defined by the IEEE 802.15.4 standard for the physical and data link protocol layers.

Zigbee Modes:
ZigBee operates in 2 modes: Non-beacon mode & Beacon mode.
Beacon mode is a fully synchronized mode in that all the device know when to coordinate with one another.  In this mode, the network "Master device" will periodically "wake-up" and send out a beacon to the devices within its network.
This beacon subsequently wakes up each slave device, who must determine if it has any message to receive.  If not, the device returns to sleep.
Non-beacon mode, on the other hand, is less synchronized, as any device can communicate with the Master as their wish. However, this way data collision can also occur. So to avoid this, the coordinator must always be awake to listen for signals, thus require more power.

How zigbee works?
ZigBee basically uses digital radio signal for devices to communicate with each other. A typical ZigBee network can be of several types of devices.Every ZigBee network must contain a network Master. A network Master/Coordinator is a device that initiates & control the network. It is aware of all the nodes within its network, and manages both the information about each node as well as the information that is being transmitted/received within the network.
 A typical Zigbee Wireless Network, (here router can be a Zigbee Shield/module)

Other devices in the network must support 802.15.4 standard's functions. They can serve as network masters, routers, or as devices interacting with real world. The figure below shows some of the ZigBee network topologies that are generally being used.  Several topologies are supported by ZigBee, including star, mesh, and cluster tree.

As can be seen, star topology is most useful when several end devices are located close together so that they can communicate with a single router node.
Mesh networking allows for redundancy in node links, so that if any node goes down, devices can find an alternative path to communicate with one another. Particularly a network administrator will decide on the shortest data transfer path.
Comparison between zigbee and bluetooth
There is a lot in common between Zigbee and Bluetooth, like both operating in the same frequency band of 2.4 GHz and belonging to the same wireless private area network (IEEE 802.15).
The ZigBee standard can operate in the 2.4GHz band or the 868MHz and 915MHz ISM (industrial, scientific & medical) bands used in Europe and the US respectively It sits below Bluetooth in terms of data rate: 250kbps at 2.4GHz (compared to Bluetooth's max. of 1Mbps) and 20-40kbps in the lower frequency bands.
The operational range is 10-75m, compared to 10m for Bluetooth (without a power amplifier), if the conditions are ideal. Another important difference between ZigBee & Bluetooth is in how their protocols work. ZigBee's uses a basic master-slave configuration suited to static star networks of many infrequently used devices that talk via small data packets. This aspect suits ZigBee to building automation and the control of multiple lights, security sensors and so on. Bluetooth's protocol is more complex because it's geared towards handling voice, images and file transfers, in Personal Area Communication. The Bluetooth, however, only allows up to 8 slave nodes in a basic master-slave piconet set-up.

ZigBee allows up to 255 slave nodes & ZigBee is broadly categorized as a low rate WPAN, as Bluetooth is.

While ZigBee is focused on control and automation, Bluetooth is focused on connectivity between laptops, PDA’s, and the like, as well as more general cable replacement.  ZigBee uses low data rate, low power consumption, and works with small packet devices; Bluetooth uses a higher data rate, higher power consumption, and works with large packet devices.  ZigBee networks can support a larger number of devices and a longer range between devices than Bluetooth.  Because of these differences, the technologies are not only geared toward different applications, they don't have the capability to extend out to other applications. In designing critical applications, ZigBee is used to designed, while Bluetooth takes much longer. Bluetooth aims at leaving away the cabling between devices that are in close proximity with each other for example between mobile phone and a laptop or desktop or a printer and a PC. Users with Bluetooth supported handsets are able to effortlessly exchange documents, calendar appointments and other files.

Technical parameters
• # Typical joining a network using Bluetooth takes three seconds while for ZigBee it is 30 milliseconds.
• # Depending on radio class, Bluetooth has a network range of 1 to 100 meters while Zigbee is up to 70 meters with a maximum network speed of 1M bit per second to 250 M bit per second respectively.
• # Bluetooth has a protocol stack size of 25KB and 28KB bytes for Zigbee.
•
 Comparing Zigbee, With Other Available Wireless Technologies

The main features of zigbee are:-
• #Dual PHY (2.4GHz and 868/915 MHz)
• #Data rates of 250 kbps (@2.4 GHz), 40 kbps (@ 915 MHz), and 20 kbps (@868 MHz)
• #Optimized for low duty-cycle applications (<0.1%)
• #CSMA-CA channel access
• #Yields high throughput and low latency for low duty cycle devices like sensors and controls
• #Low power (battery life multi-month to years)
• #Multiple topologies:  star, peer-to-peer, mesh
• #Addressing space of up to: 18,450,000,000,000,000,000 devices (64 bit IEEE address) & 65,535 networks
• #Optional guaranteed time slot for applications requiring low latency
• #Fully hand- shake protocol for transfer reliability
• #Range: 50m typical (5-500m based on environment)
Point That Must Be Considered Before Going For Zigbee Notwork Implementation:-

Zigbee has low data rate:
The radio channel data rate is a gross indicator of the throughput of the wireless connection, all else being equal. A higher data rate is not always better, depending on the requirements of the application.
Low latency of Zigbee:
Low latency is another important feature of ZigBee. When a ZigBee device is powered down (all circuitry switched off apart from a clock running at 32kHz), it can wake up and get a packet across a network connection in around 30 milliseconds. A Bluetooth device in a similar state would take around three seconds to wake up and respond. It‘s important for timing-critical messages. A sensor in an industrial plant needs to get its messages through in milliseconds.
Low power consumption of Zigbee:
ZigBee’s reliance on a central mains-powered controller minimizes the power consumption of the nodes. They will only need to turn on when they want to transfer data. There is a beacon scheme that the master uses to define slots. The nodes can then wake up, listen, synchronise to a slot and send data back. It reduces the time that the outlying nodes need to be on for.