4.2 Representation of Numbers

Explain what is meant by ‘overflow’ and ‘underflow’ in the context of binary arithmetic.

(a) Describe an arithmetic shift right operation and its effect on the binary number 10110010. (b) If this operation is performed twice on the original number, what is the resulting binary number?

Subtract the binary number 0010 from 1100 using the two’s complement method. Show your working and final answer.

Perform the following binary addition: 1101 + 0110. Show your working and state if there is an overflow.

Convert the hexadecimal number 5A to binary and denary. Show your workings.

(a) Represent the denary number -18 in an 8-bit binary using two’s complement. (b) Represent the same number using sign and magnitude representation.