Computing o level notes

Preface Underlined words have definitions in Appendix A: Definitions Bolded words r just cos i wanna emphasise 1

1 Computer Architecture In a computer, data is stored as bits . 8 bits = 1 byte, 4 bits = 1 nibble 1 Kilobyte (kB) = 10 3 bytes, Kibibyte (KiB) = 2 10 bytes Megabyte (MB) = 10 6 bytes, Mebibyte (MiB) = 2 20 bytes So on and so forth. You need to memorise until Exabyte / Exibyte Kilo → Mega → Giga → Tera → Peta → Exa Kibi → Mebi → Gibi → Tebi → Pebi → Exi Parts of a computer: Processor It executes instructions. The frequency (Hz) is how many instructions it can carry out in 1 second. Multi-core processors have > 1 processing unit and can perform more than one instruction at the same time Memory Whenever a computer needs to store data it goes here. Generally, this refers to Random Access Memory (RAM). It’s easily changed and volatile 2 . It stores data by assigning it an address . Secondary Storage It’s long term storage for large amounts of data and is non-volatile and cheaper than RAM but it’s much slower. Magnetic : More vulnerable to damage from magnetic fields, heat, impact, and natural deterioration over time. It’s heavier and bulkier than optical and solid-state media, and stores up to TBs of data. It’s cheap per GB, and is slower than solid state media. E.g. Hard disk Optical : More vulnerable to damage from scratches and natural deterioration over time, but more resistant to heat and impact. It’s portable as it’s small and light, but only stores up to GBs of data. It’s cheaper than SSDs per GB, but more ex than magnetic media, and slower than solid state media e.g. digital versatile disk (DVD) Solid-state : Most vulnerable, and most resistant to impact and temperature changes. It’s portable and lightweight due to it being small and light, and can store up to TBs of data. It’s the most expensive per GB, but faster than all other media. E.g. Solid-state drive (SSD) Data bus Bi-directional , transports data between CPU and memory Address bus Uni-directional , specifies memory address info. So when the processor wants to access data on say address 2, the processor 2 Data is lost if power supply is interrupted 1 Don’t write this tho, its not in tb and is very informal 2

will send 2 on the address bus, the data bus will return the data on address 2 in the memory to the processor. If the processor wants to override / update data at address 2, it will send data down the data bus and 2 on the address bus. The memory then updates address 2 with the data from the data bus Input devices Basically like things that provide the processor with data e.g. a microphone, a mouse, .etc Output devices Basically things that the processor outputs data to e.g. a screen, speakers, .etc Connection interfaces: Interface Use Types Speed Universal Serial Bus (USB) Powering and/or communicating with external devices Type A, B, C Micro and Mini 2.0: 480 Mbit/s 3.2: 20 Gbit/s 4: 80 Gbit/s High-Definition Multimedia Interface (HDMI) For delivering audio/video data to compatible devices (monitors, TVs) HDMI standard HDMI Mini HDMI Micro 1.3-1.4b: 10.2 Gbit/s 2.0-2.0b: 18 Gbit/s 2.1: 48 Gbit/s Peripheral Component Interconnect Express (PCIe) For communication between internal expansion cards PCI-e x1 PCI-e x4 PCI-e x8 PCI-e x16 Increases with the number of lanes , up to x16. Different lanes have diff speeds based on the version of PCIe 5.0: 4 GB/s 6.0: 8 GB/s 7.0: 17 GB/s PCIe connectors are within the motherboard. 3

2 Data representation We like to use denary in our day to day lives. Computers like binary , though. 2.1 Bin n Dec Denary to 1-byte binary: Example 169 Sum of place values: Draw a table with 8 (1-byte) columns and 2 rows, one column for each digit. In the top row write 2 n , with n = 0 at the right-hand side and increasing by one for every place it moves to the left Then fill it in from the left 169 - 2 7 = 41, so there’s 2 7 . So put 1 there. 41 - 2 6 = -23, so there isn’t 2 6 . Put 0 there. 41 - 2 5 = 9, so there is a 2 5 . Put 1 there. Rinse, repeat, and you get: 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 1 0 1 0 1 0 0 1 So, 169 10 = 1010 1001 2 So you just do the reverse for binary to denary. To find the denary value of 1010 1001 2 , 2 7 + 2 5 + 2 3 + 2 0 = 169, so 1010 1001 2 = 169 10 2.2 Hex n Bin Another one we like to use in computers is hexadecimal , since two letters can represent 1 byte. To convert Bin to Hex, you map each hexadecimal digit to its 4 bit binary equivalent: 0000 0001 0010 0011 0100 0101 0110 0111 0 1 2 3 4 5 6 7 1000 1001 1010 1011 1100 1101 1110 1111 8 9 A B C D E F So 1010 1001 2 = A9 16 , A9 16 = 1010 1001 2 So in binary u just add leading zeros (10 → 0010), split into 4 bits and use the table 2.3 Hex and Dec From Hex to Dec: It’s pretty easy. Same thing, using sum-of-place values: A9 16 , you split it to get A 16 and 9 16 . Convert it into denary to get 10 10 and 9 10 , then multiply from the right by 16 n starting with n = 0, so 10 x 16 1 + 9 x 16 0 = 169. So A9 16 = 169 10 . 4

From Den to Hex, this is where shit hits the fan . The easiest version is division by 16 . So taking 169 10 , you just repeatedly divide by 16, keeping the remainder until your quotient is 0. Turn all your remainders into hex, and read from top to bottom. E.g.: Denary Quotient Remainder 169 9 10 10 = A 16 9 0 9 10 = 9 16 Therefor 169 10 = A9 16 2.4 Two’s complement This is basically how you represent negative numbers . The idea is like a cycle: If the first bit is 0, you’re dealing with a positive number. Otherwise, you’re dealing with a negative number. So in 4-bit two’s complement, 0001 is +1, 1111 is -1. 0010 is +2, 1110 is -2. To calculate it, let the number be x . Then what you do is you take 2 n - x , where n is the number of bits. So if x = 3 10 = 011 2 (3 bits), then -3 10 = 2 3 10 - 011 2 = 8 10 - 3 10 = 5 10 = 101 2 . Hence in 3-bit two’s complement, 101 2 = -3 . The easier way is to just flip all the bits and add 1 (only do this for calculations, never for explanation on like how do you do this) So like for 011 2 , flip the bits to get 100 2 , then add 1 to get 101 2 . Or for like 0000 0101 2 (5), to get -5, flip the bits: 1111 1010 2 , add 1: 1111 1011 2 . So -5 in 8-bit two’s complement is 1111 1011 2 2.5 Text In text data, every symbol, letter, digit or space is called one character . Character encoding assigns each character a number, which allows you to transmit text in bits and bytes. The syllabus one is the (extended) American Standard Code for Information Interchange (ASCII) , whi