79. OCR A Level (H046-H446) SLR13 – 1.4 Floating point binary pa

What does the leftmost bit in a two's complement binary number represent?

• The binary point

• A fractional component

• A negative number

• A positive number

Answer explanation

The leftmost bit in a two's complement binary number represents a negative number.

How is the number 6 represented in an 8-bit binary format?

• 00001100

• 10000110

• 00000110

• 11000000

Answer explanation

The number 6 in an 8-bit binary format is represented as 00000110, which is the correct choice among the options provided.

How are fractional components stored in binary?

• By extending the number line to the left

• By using an exponent

• By using a decimal point

• By extending the number line to the right

Answer explanation

Fractional components are stored in binary by extending the number line to the right, allowing for the representation of values less than 1.

What is the binary representation of 6.5?

• 01101000

• 01100100

• 11010100

• 00110010

Answer explanation

The binary representation of 6.5 is 01100100. To convert 6.5 to binary, we separate the whole and decimal parts. The binary for 6 is 0110, and for 0.5 is 0. So, the final binary representation is 01100100.

How is the number 3.75 represented in binary?

• 00011110

• 00111100

• 01111000

• 00011100

Answer explanation

The number 3.75 is represented in binary as 00011100. This is the correct choice among the options provided.

What is the biggest positive number that can be stored in an 8-bit fixed point binary format?

• 31.75

• 255

• 127.5

• 15.875

Answer explanation

The biggest positive number that can be stored in an 8-bit fixed point binary format is 15.875, as 8 bits can represent numbers up to 2^4 - 1 = 15, and the fixed point allows for fractions like 0.875.

Why can't a third be precisely represented in binary?

• Because of rounding errors

• Because it's an irrational number

• Because binary can only represent whole numbers

• Because it requires an infinite number of bits

Answer explanation

Because it requires an infinite number of bits

What is the main advantage of floating point binary?

• It uses less memory

• It can either increase the size of the number or the accuracy

• It can store numbers with high precision only

• It can store very large numbers only

Answer explanation

The main advantage of floating point binary is that it can either increase the size of the number or the accuracy, providing flexibility in representation.

What are the two parts of a floating point binary number?

• Mantissa and exponent

• Whole number and fractional part

• Positive and negative part

• Integer and decimal part

Answer explanation

The two parts of a floating point binary number are the mantissa and exponent, which represent the fractional part and the power of 2, respectively.

How many bits are used for the mantissa in a 32-bit single precision number?

• 8 bits

• 24 bits

• 32 bits

• 16 bits

Answer explanation

In a 32-bit single precision number, 24 bits are used for the mantissa. This allows for a total of 2^24 different values to be represented in the mantissa.