Worksheet

A7.1 Number sets, bases and units

Data representation · A level · OCR H446 1.4.1, AQA 7517 4.5.1.1, Eduqas A500QS 2.3 · about 25 min

What this lesson is about

Natural, integer, rational, irrational, real and ordinal numbers; any number base; bits, bytes, kilo and kibi.

• Number sets
• Counting and measurement
• Number bases
• Bits, bytes and units

Questions 6 marks in all

1. [1 mark]Which set of numbers is the square root of 2 in, but not in the rational numbers?

   1. AIrrational numbers
   2. BNatural numbers
   3. CIntegers
   4. DOrdinal numbers

2. [1 mark]Which of these are rational numbers?

   Tick every answer that is true.

   1. A0.75
   2. B-3
   3. C22/7
   4. DThe square root of 2
   5. EPi

3. [1 mark]What are ordinal numbers used for?

   1. ATo describe a position in an ordered list, such as 1st, 2nd, 3rd
   2. BTo count how many things there are
   3. CTo measure a quantity such as a length
   4. DTo store negative values

4. [1 mark]Write the denary number 255 in base 8.

5. [1 mark]How many bytes are in 3 KiB?

6. [1 mark]What does this program print?

   n = 47
   digits = ""
   while n > 0:
       digits = str(n % 5) + digits
       n = n // 5
   print(digits)

The task: any base

Write to_base(n, base). The parameter n is a whole number, 0 or more; base is a whole number from 2 to 16. It returns the digits of n in that base as a string, using 0 to 9 then A to F, and returns "0" when n is 0. Use repeated division with // and %: you may not use bin, hex, oct or format. The loop at the bottom prints lines such as 173 in base 16 = AD.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

DIGITS = "0123456789ABCDEF"

def to_base(n, base):
    # repeated division goes here
    return ""

for n, base in [(173, 2), (173, 8), (173, 16), (0, 2), (2024, 16)]:
    print(n, "in base", base, "=", to_base(n, base))

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/a7-1-numbers-bases-and-units/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Extend to_base to refuse a base outside 2 to 16 by raising a ValueError.
2. Write from_base without DIGITS.index, using character codes instead.
3. Which set does each belong to: the number of robots on the mat, the robot's heading in degrees, 22/7, the square root of 16?