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

A repeated division and remainder algorithm can convert decimal to binary, octal, or hexadecimal.

1.                  Divide the decimal number by the desired target radix (2, 8, or 16).

2.                  Append the remainder as the next most significant digit.

3.                  Repeat until the decimal number has reached zero.

Decimal to Octal

Here is an example of using repeated division to convert 1792 decimal to octal:

Decimal to Hexadecimal

Here is an example of using repeated division to convert 1792 decimal to hexadecimal:

The only addition to the algorithm when converting from decimal to hexadecimal is that a table must be used to obtain the hexadecimal digit if the remainder is greater than decimal 9.

The addition of letters can make for funny hexadecimal values. For example, 48879 decimal converted to hex is:

П. TESTS AND ASSIGNMENTS FOR SELF-ASSESSMENT

1)        Convert 35 to the binary numbers

2)        Convert 88 to the binary numbers.

3)        Convert 300 to the binary numbers.

4)        Write the binary number 10000111 in negative denary.

5)        Write the binary number 11000111 in negative denary.

6)        Write the binary number 11000100 in negative denary.

7)        Write the binary number 11001011 in negative denary.

8)        Convert 10100011 from binary to decimal.

9)        Convert 101101 from binary to decimal.

10)    Convert 110100101010 from binary to decimal.

11)    Convert 11101111 from binary to decimal.

12)    Convert 01000010 from binary to decimal.

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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