CS chapter 1

• Number systems used in computer science: binary, denary, and hexadecimal
• Binary number system is based on the number 2, using only the values 0 and 1
• Denary number system uses ten separate digits, 0-9, and is known as a base 10 number system
• Binary number with eight digits would have headings: 128, 64, 32, 16, 8, 4, 2, 1
• Converting binary to denary involves adding the column value each time a 1 appears in a binary number column
• Example conversions from binary to denary: 11101110 = 238, 011110001011 = 19314, 0011000111100110 = 12774
• Converting denary to binary can be done by successive subtraction of powers of 2 or by successive division by 2
• Example conversions from denary to binary: 142 = 10001110, 59 = 00111011, 35000 = 1000100011011000
• Converting from binary to hexadecimal involves splitting the binary number into groups of 4 bits and converting each group into the equivalent hexadecimal digit using Table 1.1
• Converting from hexadecimal to binary is done by taking each hexadecimal digit and writing down the 4-bit code which corresponds to the digit
• Converting from hexadecimal to denary involves multiplying each hexadecimal digit by its heading value (4096, 256, 16, 1) and adding the totals together to get the denary number
• Converting from denary to hexadecimal requires successive division by 16 until reaching 0, then reading the remainders in reverse order to get the hexadecimal number
• The hexadecimal system uses 16 different 'digits' to represent each value, including numbers 0-9 and letters A-F
• A computer can work with binary data, but hexadecimal is more convenient for humans as one hex digit represents four binary digits
• Media Access Control (MAC) addresses uniquely identify devices on a network, usually made up of 6 groups of two hexadecimal digits
• MAC addresses consist of the manufacturer's identity number and the device's serial number
• Internet Protocol (IP) addresses are given to each device connected to a network
• Devices made by Cisco 00 – a0 – c9 identify devices made by Intel
• Each device connected to a network is given an Internet Protocol (IP) address
• An IPv4 address is a 32-bit number written in denary or hexadecimal form
• IPv4 has been improved upon by the adoption of IPv6
• An IPv6 address is a 128-bit number broken down into 16-bit chunks, represented by a hexadecimal number
• HyperText Mark-up Language (HTML) is used when writing and developing web pages
• HTML isn’t a programming language but is simply a mark-up language
• HTML uses <tags> to bracket a piece of text for example, <h1> and </h1> surround a top-level heading
• HTML colour codes are used to represent colours of text on the computer screen
• The # symbol always precedes hexadecimal values in HTML code
• There are 16,777,216 possible colours represented by 256 values for red, green, and blue
• Addition of binary numbers
• Binary addition involves carry and sum values
• Carrying occurs whenever the sum is greater than 1
• Overflow error can occur when the sum exceeds the maximum value that can be stored
• Logical binary shifts
• Logical shift means moving the binary number to the left or right
• Each shift left is equivalent to multiplying the binary number by 2 and each shift right is equivalent to dividing the binary number by 2
• There is a limit to the number of shifts that can be carried out if the binary number is stored in an 8-bit register
• Shifting the original binary number 00010101 four places left results in losing the left-most 1-bit
• In an 8-bit register, the result of 21 × 2^4 is 80, which is incorrect due to exceeding the maximum number of left shifts possible
• The denary number 200 in binary is 11001000 in an 8-bit register
• Shifting the bits in the register one place to the right results in the left-most bit being lost