Floating point numbers in binary

Two’s complement can be used to represent negative binary numbers.

Convert the denary number-124 into an 8-bit two’s complement binary number.

State one other way to represent negative binary numbers.

Convert the denary number 298 into hexadecimal.

The binary number 10011101 0110 is stored in normalised floating point form with an 8-bit mantissa and a 4-bit exponent both written in two’s complement.

Convert this binary number into denary.

You must show your working.

The binary number 00001011 0111 is represented in unnormalised floating point form with an 8-bit mantissa and a 4-bit exponent both written in two’s complement.

Convert this binary number into a normalised floating point binary number, represented using an 8-bit mantissa and 4-bit exponent format.

You must show your working.

Convert the denary number 189 to hexadecimal.

Convert the unsigned binary number 1010101111 to hexadecimal.

Negative binary values can be represented using either sign and magnitude or two’s complement.

Convert the denary number-107 to an 8-bit binary number using sign and magnitude.

Convert the denary number-107 to an 8-bit binary number using two’s complement.

Give one advantage of storing values using two’s complement instead of sign and magnitude.

Show how the denary value-15.75 can be represented as a normalised floating point binary number using 8 bits for the mantissa and 4 bits for the exponent.

You must show your working.

The normalised floating point binary number 0100 1110 is stored using 4 bits for the mantissa and 4 bits for the exponent, both in two’s complement.

Convert this number to denary.

You must show your working.

Complete each of the following sentences relating to the storage of floating point binary numbers with an appropriate word.

Increasing the number of bits used for the mantissa increases the........ of the number that can be stored.

Increasing the number of bits used for the exponent increases the........ of the number that can be stored.

Convert the hexadecimal value B7E to a binary number.

110010101 is a binary number that is represented using sign and magnitude.

Convert this binary number to a denary number.

Complete this binary subtraction. Both numbers are 8-bit integer values represented using two’s complement.

Show the result in the same format and show your working.

0110 1101 – 0011 0100

The normalised floating point number 1010 1110 is stored using 4 bits for the mantissa and 4 bits for the exponent, both in two’s complement.

Give the denary version of this number, showing your working.

Table 3 here shows floating point numbers that are stored using 6 bits for the mantissa and 3 bits for the exponent, both in two’s complement.

Tick (✓) one box in each row to state whether each number is normalised or not normalised.

Convert the denary number 231 to an unsigned 8-bit binary number.

Convert the hexadecimal number 6F to an unsigned 8-bit binary number.

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.

Give the normalised version of this number, showing your working.

Convert your answer to part (i) to denary, showing your working.

Add together the two numbers below. Both numbers are stored in normalised floating point format, using 6 bits for their mantissa and 4 bits for their exponent which are both in two’s complement. Show the result in the same format and show your working.

Convert the denary number −119 to an 8-bit binary number with two’s complement representation.

Convert the unsigned binary number 1101101 to hexadecimal.

Convert the denary number 171 to hexadecimal.

Convert the hexadecimal number A6 to binary.

Show how the denary value −9.125 can be represented in normalised floating point format, using 8 bits for the mantissa and 4 bits for the exponent, both in two’s complement.

Show the result of applying an XOR mask of 1100 0111 to the byte 0101 1101.

Byte 0101 1101

Describe a mask that could be applied to an 8-bit number to ensure that:

• the most significant bit is always set to 1

• all other bits remain unchanged.

Show how the binary number 01011110 is represented in hexadecimal.

Show how the hexadecimal number 9B is represented in denary.

Show how the denary number −87 is represented in sign and magnitude binary.

Complete the following binary subtraction. Show your working.

The floating point binary number 010011 011 consists of a 6-bit mantissa and 3-bit exponent, both represented in two’s complement. Convert the number to denary, showing your working.

Show the denary number −5.25 in floating point binary form representing the mantissa and exponent in two’s complement, using as few bits as possible. Show your working.

Convert the binary number shown below to hexadecimal.

0011011100001111

The number below is represented in floating point format with a 5-bit mantissa in two’s complement followed by a 3-bit exponent in two’s complement. Calculate the denary value of the number, showing your working.

01001 010

The numbers below are represented in floating point format with a 5-bit mantissa in two’s complement followed by a 4-bit exponent in two’s complement. Normalise the numbers shown below, showing your working.

00011 0010

11100 0110

Show the byte below after having an AND applied with the masking byte.

Show the byte below after having an OR applied with the masking byte.