Binary

Question 1

What do computers use binary to do?

Answer 1

• To represent data, such as numbers, text, sound and graphics
• To program instructions

Question 2

What is 4 bits known as?

Answer 2

A nibble

Question 3

What is 8 bits known as?

Answer 3

A byte

Question 4

(Exam-style question)

Explain one reason why all instructions and data used by a computer are represented in binary. (3)

Answer 4

• A processor consists of billions of transistors, each having just two states, on/off
• The on/off states of a transistor represent the binary digits 1/0

Question 5

(Exam-style question)

Describe a ‘bit’. (2)

Answer 5

• A bit is short for binary digit, the smallest unit of data in a computer
• A bit has a single binary value, either 0 or 1

Question 6

(Exam-style question)

Give one reason why a computer doesn’t need to know what a binary pattern represents. (1)

Answer 6

The microprocessor hardware only operates on bits, so it has no concept of type or representation

Question 7

(Exam-style question)

Write an arithmetic expression to show that 256 different colours can be represented in 8 bits. (1)

Answer 7

2⁸ = 256 colours

Question 8

What can denary numbers also be called?

Answer 8

Decimal numbers

Question 9

(Exam-style question)

Explain one reason why the denary number 256 cannot be represented in an 8-bit binary pattern. (2)

Answer 9

• The number would be represented in binary as 100000000
• You would need 9 bits to store it

Question 10

Convert the following denary numbers into 8-bit binary numbers:

a) 203
b) 241
c) 79
d) 100

Answer 10

a) 11001011
b) 11110001
c) 01001111
d) 01100100

Question 11

Convert the 8-bit binary pattern 11011001 into a denary number.

Answer 11

217

Question 12

List two ways of representing signed integer numbers.

Answer 12

• Two’s complement
• Sign and magnitude

Question 13

What happens if the most significant bit of a two’s complement or sign and magnitude pattern is 1?

Answer 13

The number will have a negative value

Question 14

(Example)

Convert -10 to binary two’s complement.

Answer 14

• Write out the positive number (+10) in binary: 00001010
• Flip all the bits: 11110101
• Add 1 (00000001) to the result. This gives: 11110110
• Therefore, -10 in two’s complement is 11110110

Question 15

(Exam-style question)

Convert the denary number -54 to 8-bit binary two’s complement representation. (3)

Answer 15

11001010

Question 16

(Exam-style question)

Give the denary value of the 8-bit two’s complement number 11101111. (3)

Answer 16

-17

Question 17

(Exam-style question)

Convert the denary number -94 to a binary pattern using sign and magnitude representation. (2)

Answer 17

11011110

Question 18

(Exam-style question)

Give the result of adding 00101011 and 00010111. (2)

Answer 18

01000010

Question 19

(Exam-style question)

Add the following 8-bit binary numbers:

01010111 + 01011111

Give your answer in 8-bit binary form. (2)

Answer 19

10110110

Question 20

(Exam-style question)

Give the result of applying a logical shift left, 2 places, to the 8-bit binary pattern 00010100. (1)

Answer 20

01010000

Question 21

(Exam-style question)

Give the result of applying a logical shift right, 3 places, to the 8-bit binary pattern 10111000. (1)

Answer 21

00010111

Question 22

(Exam-style question)

Give the result of applying an arithmetic shift right, 1 place, to the 8-bit binary pattern 10001000. (1)

Answer 22

11000100

Question 23

(Exam-style question)

Give the result of applying an arithmetic shift left, 1 place, to the 8-bit binary pattern 11101100. (1)

Answer 23

11011000

Question 24

(Exam-style question)

Describe one difference between a logical and an arithmetic shift. (2)

Answer 24

• An arithmetic shift preserves the most significant bit
• A logical shift always fills the vacated bits with 0s

Question 25

# **(Exam-style question)** The binary bit pattern 10101101 is equal to the denary number 173. Explain the effect of performing a logical shift right of two places on the binary number 10101101, and state the denary number equivalent after the shift. (3)

Answer 25

* The binary number becomes 00101011 after the two-place logical right shift * The new binary number's denary equivalent is 43 * In a two-place logical right shift, the binary number is divided by 4; the result of dividing 173 by 4 is 43.25. * The right shift produces an imprecise result because it discards the two bits on the right of the binary number, effectively rounding it down to the nearest whole number

Question 26

What happens to a binary number that has been shifted right one place?

Answer 26

It has been divided by 2

Question 27

What type of binary numbers do arithmetic shifts operate on?

Answer 27

Two's complement binary

Question 28

What type of binary numbers do logical shifts operate on?

Answer 28

Sign and magnitude binary

Question 29

# **(Exam-style question)** Define the term 'overflow'. (2)

Answer 29

An error that occurs when a calculation produces a result that is greater than what the computer is able to store, or is greater than the number of bits available to store it

Question 30

# **(Exam-style question)** State two consequences of an overflow error. (2)

Answer 30

* The program might crash * Continued use of an incorrect result in calculations will cause further errors

Question 31

# **(Exam-style question)** Explain one reason why the result of adding two 16-bit binary patterns together must be 16 bits in length. (2)

Answer 31

The registers inside the machine that hold the original patterns have a fixed length, so they cannot hold more than 16 bits

Question 32

# **(Exam-style question)** Describe one way an overflow error can be caused by shifting the 8-bit binary pattern 11000011 left by one position. (2)

Answer 32

* Shifting left the original pattern 11000011 gives 10000110 * The original 1 in the most significant bit is shifted out, therefore it uses a position that does not exist in the register

Question 33

# **(Exam-style question)** Convert the 8-bit binary number 10110111 to hexadecimal. (1)

Answer 33

B7

Question 34

# **(Exam-style question)** Convert the hexadecimal number E9 to 8-bit binary. (1)

Answer 34

11101001

Question 35

What are some of the uses of hexadecimal notation?

Answer 35

* Used to help people deal with long binary digits as they are much shorter in hexadecimal * Error code numbers are usually given in hexadecimal when a computer malfunctions * Used to represent numerical values in assembly language

Question 36

What is the number of bits true colour uses to code every available colour variation?

Answer 36

24 bits

Question 37

Each colour is represented by three 8-bit binary numbers that can be simplified to three 2-digit hexadecimal ones. What is the benefit of this?

Answer 37

It is much easier to remember and enter the six digits of the hexadecimal number

Question 38

# **(Exam-style question)** Explain why hexadecimal numbers are sometimes used to represent values stored in computers, even though computers do not use hexadecimal numbers. (2)

Answer 38

* Large binary numbers can be complicated to read and work with * Binary numbers can be simplified by writing them in hexadecimal as fewer numbers are needed, making them easier to read and memorise

Question 39

What base are hexadecimal numbers in?

Answer 39

Base 16