Converting between denary & hexadecimal

Convert the denary number 189 into an 8-bit binary number.

Convert the denary number 189 into a hexadecimal value.

Convert the hexadecimal value E4 into a denary number.

Explain the effect that a right shift of three places will have on a positive binary number.

Show the subtraction of these two floating point binary numbers.

Both numbers are stored in a normalised floating point format, using 6 bits for the mantissa and 4 for exponent.

You should show your result in the same format.

Show your working out.

011010 0011 – 010010 0010

Final 6-bit mantissa........

Final 4-bit exponen t........

Show the result of applying a bitwise AND mask of 1010 1110 to the byte 1010 0011.

State the purpose of the bitwise AND mask.

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 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 denary number 188 to an unsigned 8-bit binary number.

Convert the denary number 188 to hexadecimal.

Convert the denary number −44 to an 8-bit binary number with sign and magnitude representation.

Convert the denary number −44 to an 8-bit binary number with two’s complement representation.

Explain how, using bit shift, the unsigned binary number 00101100 can be divided by 4.

Demonstrate subtraction on the two numbers below, both stored in normalised floating point format, using 6 bits for their mantissa and 4 for their exponent. Show the result in the same format. Show your working.

010010 0100 - 010010 0010