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IGCSE Edexcel Computer Science > Binary > Flashcards

Binary Flashcards

(areas covered: using binary, unsigned integers, two's complement and sign and magnitude signed integers, binary addition, logical and arithmetic shifts, overflow, hexadecimal)

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1
Q

What do computers use binary to do?

A
  • To represent data, such as numbers, text, sound and graphics
  • To program instructions
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2
Q

What is 4 bits known as?

A

A nibble

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3
Q

What is 8 bits known as?

A

A byte

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4
Q

(Exam-style question)

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

A
  • 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
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5
Q

(Exam-style question)

Describe a ‘bit’. (2)

A
  • 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
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6
Q

(Exam-style question)

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

A

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

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7
Q

(Exam-style question)

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

A

2⁸ = 256 colours

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8
Q

What can denary numbers also be called?

A

Decimal numbers

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9
Q

(Exam-style question)

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

A
  • The number would be represented in binary as 100000000
  • You would need 9 bits to store it
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10
Q

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

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

A

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

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11
Q

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

A

217

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12
Q

List two ways of representing signed integer numbers.

A
  • Two’s complement
  • Sign and magnitude
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13
Q

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

A

The number will have a negative value

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14
Q

(Example)

Convert -10 to binary two’s complement.

A
  • 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
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15
Q

(Exam-style question)

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

A

11001010

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16
Q

(Exam-style question)

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

A

-17

17
Q

(Exam-style question)

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

A

11011110

18
Q

(Exam-style question)

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

A

01000010

19
Q

(Exam-style question)

Add the following 8-bit binary numbers:

01010111 + 01011111

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

A

10110110

20
Q

(Exam-style question)

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

A

01010000

21
Q

(Exam-style question)

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

A

00010111

22
Q

(Exam-style question)

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

A

11000100

23
Q

(Exam-style question)

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

A

11011000

24
Q

(Exam-style question)

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

A
  • An arithmetic shift preserves the most significant bit
  • A logical shift always fills the vacated bits with 0s
25
Q

(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)

A
  • 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
26
Q

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

A

It has been divided by 2

27
Q

What type of binary numbers do arithmetic shifts operate on?

A

Two’s complement binary

28
Q

What type of binary numbers do logical shifts operate on?

A

Sign and magnitude binary

29
Q

(Exam-style question)

Define the term ‘overflow’. (2)

A

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

30
Q

(Exam-style question)

State two consequences of an overflow error. (2)

A
  • The program might crash
  • Continued use of an incorrect result in calculations will cause further errors
31
Q

(Exam-style question)

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

A

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

32
Q

(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)

A
  • 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
33
Q

(Exam-style question)

Convert the 8-bit binary number 10110111 to hexadecimal. (1)

A

B7

34
Q

(Exam-style question)

Convert the hexadecimal number E9 to 8-bit binary. (1)

A

11101001

35
Q

What are some of the uses of hexadecimal notation?

A
  • 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
36
Q

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

A

24 bits

37
Q

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?

A

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

38
Q

(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)

A
  • 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
39
Q

What base are hexadecimal numbers in?

A

Base 16

IGCSE Edexcel Computer Science (23 decks)

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