Methodological Instructions

Theme: Conversion between number system

Objective: 10.2.1.1 Convert decimal numbers to binary numbers and vice versa

Assessment criteria

·                    Translates numbers from decimal to binary

·                    Translations of the number of one number system to another

Basic Level:

Multiplication table (7-9 grade)

Key words and phrases:

Numeral system, binary, hexadecimal, octal and decimal system alphabet and how translate between numeral systems and vice versa, Numeral system is a ____

Translate number from binary system to decimal system…

I.                   THEORY

Converting denary to binary: Method 2

There are two methods for converting a denary (base 10) number to binary (base 2). This is method two.

Take off the biggest 2ⁿ value you can

Remove the 2ⁿ numbers from the main number and mark up the equivalent 2ⁿ column with a 1. Work through the remainders until you reach zero. When you reach zero, stop and complete the final columns with 0s.

First set up the columns of base 2 numbers. Then look for the highest 2ⁿ number that goes into 84.

1.         Set up the columns of base 2 numbers

2.         Find the highest 2ⁿ number that goes into 84. The highest 2ⁿnumber is 26 = 64

3.         84 – 64 = 20. Find the highest 2ⁿ number that goes into 20. The highest 2ⁿ number is 24 = 16

4.         20 - 16 = 4. Find the highest 2ⁿ number that goes into 4. The highest 2ⁿ number is 22 = 4

5.         4 - 4 = 0

6.         Mark up the columns of base 2 numbers with a 1 where the number has been the highest 2ⁿ number, or with a 0:

Result: 84 in denary is equivalent to 1010100 in binary.

To check that this is right, convert the binary back to denary:

(1 x 64) + (0 x 32) + (1 x 16) + (0 x 8) + (1 x 4) + (0 x 2) + (0 x 1) = 84

П. TESTS AND ASSIGNMENTS FOR SELF-ASSESSMENT.

1.      Convert binary numbers to denary

a) 00011000 _______________________________________________________________

b) 00000101 _______________________________________________________________

c) 00010110 _______________________________________________________________

d) 01101011 _______________________________________________________________

e) 01111000 _______________________________________________________________

f) 10100100 _______________________________________________________________

g) 10100101 _______________________________________________________________

h) 10111100 _______________________________________________________________

i) 11010111 _______________________________________________________________

j) 11100110 _______________________________________________________________

k) 11111010 _______________________________________________________________

Answers:

a)      24

b)      5

c)      22

d)      107

e)      120

f)       164

g)      165

h)      188

i)       215

j)       230

k)      250

VISUAL AIDS AND MATERIALS.

1.             Slides

2.             Introducing binary https://www.bbc.com/bitesize/guides/zwsbwmn/revision/7

3.             Different number systems http://www.anastasi-shherbakova.narod.ru/p7aa1.html

4.             Converting Denary to Binary  http://www.zaurtl.ru/UkVT/UKVT6.html

5.             Converting Binary to n-based system  https://www.youtube.com/watch?v=cPOgHCqecxY

6.             Abilities of the Calculator program: http://www.compgramotnost.ru/windows-7/kalkulyator-windows-7

7.             Converting Denary to Binary https://www.youtube.com/watch?v=70lM1qAD5u4

8.             Denary to Binary: Division https://www.sqa.org.uk/e-learning/CompArch01CD/page_10.htm

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