This assessment consists of two questions. The first one looks into how computers represent data and how we can interconvert these representations. The second question looks at finding a Boolean expression for an output variable given a truth table and then drawing a logic circuit diagram using a simulator and testing for errors.
Question 1 – Data Representation in Computer [3 + 4 marks]
(a) Using the rules of overflow, prove that adding -107 and -40 is not possible in an 8-bit computer using 2’s complement integers. Show all workings.
(b) A 16-bit floating point representation is defined like this: 1 bit for sign, 6 bits for exponent and 9 bits for significand. Floating point number must be normalized (in the form 0.1… × 2exp). Exponent is stored in one’s complement representation. Significand is stored as is without any hidden bits. Find out the smallest positive number that can be stored in such a system. Work out its (i) 16 bit binary (ii) equivalent base 10 number in scientific notation. Show all workings.