Quiz

A phone number can start with 0 and contain a space, and nobody does arithmetic with it, so it is text: a string. Storing it as an integer would drop the leading 0.

Split into nibbles from the right: 1011 is 11, which is B, and 0110 is 6, giving B6. 182 is the denary value, not the hexadecimal.

The first digit is worth 16s and F is 15, so 2 × 16 + 15 = 47.

+20 is 0001 0100. Flipping every bit gives 1110 1011, and adding 1 gives 1110 1100. Check: −128 + 64 + 32 + 8 + 4 = −20. 1001 0100 is −20 in sign and magnitude, and 1110 1011 forgets to add 1.

The most significant bit is worth −128 and the other seven bits add up to at most 127, so the range is −128 to 127. −127 to 127 is the range of sign and magnitude, which wastes a pattern on a second zero.

192 + 80 = 272, which is more than 255, the largest number 8 bits can hold. A carry goes out of the most significant bit, so the result overflows; the 8 bits left (0001 0000) do not hold the right answer.

The mantissa is 0.1010000, which is 0.625. The exponent is 2, so move the binary point 2 places right: 10.1, which is 2.5.

A normalised mantissa starts with two different bits: 01 if positive or 10 if negative. 1011 0000 starts 10, so it is a normalised negative number. Mantissas starting 00 or 11 can be shifted left to gain precision.

Shift the mantissa left 2 places so it starts 01: 0110 0000. Moving the binary point 2 places right makes the number 4 times bigger, so take 2 off the exponent to keep the same value: 6 − 2 = 4, which is 0100.

Mantissas can only be added when their binary points line up, which means the exponents must match. Shift right the mantissa of the number with the smaller exponent, increasing that exponent until they are equal. Normalisation comes last, on the result.

OR with 1 always gives 1, and OR with 0 leaves a bit as it was, so 1000 0000 sets just the MSB. AND with 1000 0000 would clear the other bits, and XOR would flip the MSB rather than always setting it.

Each bit moves 2 places left and 0s fill the gap on the right, giving 0011 0000. Each place left doubles an unsigned number, so 2 places multiply by 4: 12 × 4 = 48.

With 7 bits, ASCII has room for only 128 characters, enough for English but not for other alphabets and symbols. Unicode uses more bits per character, so it can represent over a million characters. It often uses more storage, not less.

77 = 64 + 8 + 4 + 1, so there are 1s in the 64, 8, 4 and 1 columns: 0100 1101. 0100 1110 is 78 and 0100 1011 is 75.

200 = 12 × 16 + 8. Twelve is C, so the answer is C8. In binary, 200 is 1100 1000, and the two nibbles are C and 8. 8C has the digits the wrong way round.

75 is 0100 1011. Flipping the bits and adding 1 gives 1011 0101 (−75). 0011 0010 + 1011 0101 = 1110 0111, which is −128 + 64 + 32 + 4 + 2 + 1 = −25. 1001 1001 is −25 in sign and magnitude, and 1110 0110 comes from forgetting to add 1.

Line up the exponents first: 0.75 has the smaller exponent, so shift its mantissa right 2 places to 0001 1000 with exponent 2. Adding gives 0110 1000, exponent 2, which is 0.8125 × 4 = 3.25. Adding the mantissas without lining them up gives 1011 0000, which would be a negative number.