data representation

• Unicode has enough capacity to represent a wealth of different languages, symbols and emoji.
• Primitive data types include Integer, Real/Floating Point, Character, String, and Boolean.
• Unicode solves the problem of ASCII’s limited character set.
• 128 characters is sufficient for standard letters, numbers and symbols, but ASCII encounters trouble when computers need to represent other languages with different characters.
• Unicode uses a varying number of bits, allowing for over 1 million different characters, many of which have yet to be allocated.
• Integer is a whole number that includes zero and negative numbers, but cannot have a fractional part.
• Real numbers are positive or negative numbers which can, but do not necessarily, have a fractional part.
• Character is a single symbol used by a computer, including the letters A to Z, the numbers 0 to 9 and hundreds of symbols like %, £ and 。
• String is a collection of characters, which can be used to store a single character or many characters in succession.
• Boolean data type values are restricted to True and False.
• Integers can be represented in binary, hexadecimal and decimal.
• Negative numbers can be represented in binary using sign magnitude or two’s complement.
• Addition and subtraction of binary integers can be performed.
• Positive integers can be represented in hexadecimal.
• Positive integers can be converted between binary, hexadecimal and decimal.
• Character sets are used to represent text, including ASCII and Unicode.
• Data is always stored in binary by computers, but the way in which data is represented varies between different types of data.
• In this case, the exponent is 5.
• Floating point numbers can be split into two parts: mantissa and exponent.
• The mantissa is always taken to have the binary point after the most significant bit.
• Combining the three parts, the binary point needs to be moved five places to the right, giving us 110010.0111.
• Floating point binary can be thought of as being like scientific notation.
• One way to convert from hexadecimal to decimal is to first convert to binary, as explained above, and then convert from binary to decimal.
• In binary, a sign of 0 represents a positive number and a 1 represents a negative number.
• The hexadecimal number 4E7F equals 20095 in decimal.
• In the case of a mantissa and exponent, the mantissa is 6.67 and the exponent is -11.
• The mantissa in this case is 1.100100111.
• When combined, the mantissa and exponent provide all the information needed to work out the actual value being represented.
• The exponent is converted to decimal using the method explained earlier.
• In the case of scientific notation, the mantissa is shifted 11 times from the decimal point.
• Another way to convert from hexadecimal to decimal is to use the place values of hexadecimal to convert directly to decimal.
• To convert hexadecimal to binary, first convert each hexadecimal digit to a decimal digit and then to a binary nybble before combining the nybbles to form a single binary number.
• Strings can be used to store text and phone numbers which start with a 0, which numeric data types like integers would cut off.
• Flipping all the bits and adding one gives us 11111001.
• Checking the result, -16 + 8 + 4 = -4, so the calculation is correct.
• Place values in hexadecimal start with 1 (16 0) and go up in powers of 16.
• The two’s complement numbers are then added using the same technique for adding that was explained earlier before the result can be read off as 11100.
• Hexadecimal makes use of the characters A-F to represent 10-15.
• The binary byte representing 7 is 00000111.
• Decimal 0-9, A-F are represented by the numbers 0-15 in hexadecimal.