A-Level Binary Numbers

Represent the denary value of -17 as an 8-bit binary number using sign and magnitude.

Convert the denary value of -17 into an 8-bit binary number using 2s complement.

Perform the binary subtraction shown. The binary values are represented using 2s complement.

Using normalised floating point binary representation using 4-bits for the mantissa and 4-bits for the exponent, represent the denary value of 1.75.

Match these bitwise operations with their arithmetic equivalent.

• multiply by 4

• Left Shift 1

• divide by 2

• Right Shift 1

• multiply by 2

• Bitwise AND using mask of all 0s

• divide by 4

• Right Shift 2

• multiply by 0

• Left Shift 2

Perform a bitwise XOR operation on the binary value of 11001100 using a mask of 11111111

Organise these floating point binary values into those which are normalised and those which are not.

Groups:

(a) Normalised

,

(b) Not Normalised

• 01010101

• 00110011

• 01001001

• 10110011

• 11001100

• 11110000

• 10101101

• 00001111

Convert the following floating point binary number into its denary equivalent. It uses 5 bits for the mantissa and 3-bits for the exponent.

10100111

The floating point number 001101 0100 is stored using 6 bits for the mantissa and 4 bits for the exponent, both in two’s complement. This number is not normalised.

Normalise this floating point number, giving your answer in the same format.

Show how the denary value -12.75 can be represented as a normalised floating point binary number using 8-bits for the mantissa and 4-bits for the exponent.