Flashcards

Integer, real (floating point), character, string and Boolean.

It may start with 0 or contain spaces, which an integer would lose, and it is never used in calculations.

0 to 255. In general, n bits hold 0 to 2ⁿ − 1.

64 + 16 + 8 + 2 = 90.

Each hex digit stands for 4 bits, so it is a shorter way to write binary that is easier for people to read and remember, with fewer mistakes.

3 × 16 + 12 = 60.

Split the bits into groups of 4 from the right, then write each group as one hex digit. 0101 1010 is 5A.

The most significant bit is the sign (1 for negative) and the remaining bits hold the size. −90 is 1101 1010.

Write the positive number in binary, flip every bit, then add 1. −90: 0101 1010 → 1010 0101 → 1010 0110.

−128 to 127. The most significant bit has place value −128.

Binary addition and subtraction work directly, so no extra hardware is needed. There is only one representation of zero, so it holds one more number (−128).

Add the two's complement of the second number, and ignore any carry out of the most significant bit.

When the result of a calculation is too large to fit in the number of bits available, so the stored result is wrong.

The mantissa holds the significant digits of the number. The exponent says how many places to move the binary point: value = mantissa × 2^exponent.

More mantissa bits give more precision. More exponent bits give a greater range.

The first two bits of the mantissa are different: 01 for a positive number, 10 for a negative number.

To store each number as precisely as possible in the bits available, and so each value has only one representation.

Make the exponents the same (shift right the mantissa of the number with the smaller exponent), add the mantissas (to subtract, add the two's complement), then normalise the result.

A logical shift fills the gap with 0. An arithmetic shift copies the sign bit, so a two's complement number keeps its sign and is divided by 2.

An AND mask keeps the bits where the mask is 1 and clears the rest. An OR mask sets bits to 1. An XOR mask flips the bits where the mask is 1.

ASCII uses 7 bits for 128 characters, mostly English. Unicode uses up to 32 bits per character, enough for every writing system and emoji, and its first 128 codes match ASCII.