1 - Theory of Computer Science / Binary numbers

## Exam Questions - Binary Numbers

Binary questions can come in a number of different forms. Some will ask you to explain why binary is used, some will ask for a straight forward conversion and some will link the binary conversions to ASCII or Registers. Here are a few different examples of what to expect.

## Example Question 1

Reveal Answers

**8**

(a)Question 8 part (a) may initially look like a bigger question than it actually is. The question explains that you have two registers which it uses to display the hours and minutes on a digital clock. Register A represents the hours and register B represents the minutes. You are asked to say what time the clock is displaying based on the binary in the two registers.

(a)

All this question requires you to do is two very simple Binary to Denary conversions:

**Hours**= 00010010 = 16 + 2 =

**18**

Minutes =00110101 = 32 + 16 + 4 + 1

Minutes =

**= 53**

(b)Question 8 part (b) is asking you to do the reverse of part (a). This time you are required to show the time '7:30' in the two registers. This essentially means that in register C you need to write down the binary for the number 7 and in register D you need the binary for the number 30.

(b)

**Register C**= 7 =

**00000111**

Register D= 30 =

Register D

**00011110**

## Example Question 2

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**10**

(a)Question 10 (a) is asking for a simple conversion of the denary number 431 into binary. The question lets us know that we should use a 12 bit binary number and even gives you a table to help you get started. We would suggest answering this question by first adding the table headings like this:

(a)

2048 |
1024 |
512 |
256 |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |

Value |

Next you would put 1s in each of the boxes required to add up to 431:

**Answer =**2048 |
1024 |
512 |
256 |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |

O |
O |
O |
1 |
1 |
O |
1 |
O |
1 |
1 |
1 |
1 |

Remember that the question specifically asked for a 12 bit binary number so you must include the 3 0s on the left side of the binary number.

## Example Question 3

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**1**

Question 1 simply requires you to list the units of memory in correct order from smallest to largest. The question has 4 empty spaces and even gives you the 4 units to add, you simply have to put them in the correct order. The correct order for this question is:

- Bit
- Nibble
- Byte
- Kilobyte (kB)
- Megabyte (MB)
- Gigabyte (GB)
- Terrabyte (TB)

## Example Question 4

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**3.**

**(a)**Question 3 (a) shows you the time 02:31:58. It explains that it uses three registers, one register stores the seconds in binary, another register stores the minutes in binary and the third register stores the hours in binary.

This question is simply asking you to convert the denary values of the provided time into binary. 3 labeled registers are provided for your answer.

Answers

Answers

**(b)**Question 3(b) is essentially the reverse of part (a). Here you are given three registers (Labeled Hours, Minutes and Seconds) which you need to convert the binary that they contain into denary. The results of the conversion should be placed into the provided box in the correct space.

**Answer:**

## Example Question 5

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**1**

Question 1 is a fill in the blanks style question. There are 6 spaces to be filled but you are given 8 possible words to fill them. As stated in the question, not all words need to be used.

**Correct Answer:**

As Humans, we process

**Analogue**data, but a computer cannot process this type of data. For a computer to be able to process data it needs to be converted to

**Digital**data.

As Humans, we mostly use a

**Denary**Number system; this is a base

**10**number system.

Computers use a

**Binary**number system; this is a base

**2**number system.

1 mark is awarded for each correct answer.

**(b)**Question 3(b) is essentially the reverse of part (a). Here you are given three registers (Labeled Hours, Minutes and Seconds) which you need to convert the binary that they contain into denary. The results of the conversion should be placed into the provided box in the correct space.

**Answer:**

## Example Question 6

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**3**

**(a)**Question 3 (a) asks you to explain the difference between the binary number system and the Denary number system. There are four marks on offer here but only 2 marks can be given for your explanation of each number system.

**Answers**

- The Binary number system is base 2
- The Denary number system is base 10
- The Binary number system uses 0 and 1 values
- The Denary number system uses values from 0 to 9
- The Binary number system has units / placeholders / column headings that increase by the power of 2
- The Denary number system has units / placeholders / column headings that increase by the power of 10
- Binary has more digits for the same value OR Denary has less digits for the same value

**(b)**Question 3 (b) is an unusual one as it asks you to explain how you would convert a binary number into Denary rather than just doing the calculation.

With 5 marks on offer you would be awarded 1 mark for any 5 of the following points (Or other logical explanations)

**A**

**nswers**

- Correct column headings / Place holders by example
- Correctly place a 1 or 0 for each column
- Identify the columns to be added
- Add together the (Denary) values identified
- This will give a total which is the Denary number / answer
- Answer is 10

## Example Question 7

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