# Lesson Notes By Weeks and Term - Junior Secondary School 2

CONVERSION OF NUMBER BASE

SUBJECT: ICT

CLASS:  JSS 2

DATE:

TERM: 1st TERM

WEEK 9

TOPIC: CONVERSION OF NUMBER BASE

DECIMAL AND BINARY

Conversion of decimal to binary

To convert decimal to binary divide decimal number by 2 till you get to zero (0)

Example 1: Convert 3710  to binary

Solution

 Division Quotient Reminder 372 18 1 182 9 0 92 4 1 42 2 0 22 1 0 12 0 1

3710 =   1001012

Example 2: Convert 9310  to binary

Solution

 Division Quotient Reminder 932 46 1 462 23 0 232 11 1 112 5 1 52 2 1 22 1 0 12 0 1

9310  = 10111012

Example 3:  Convert 25.62510  into a binary number

SOLUTION

 Division Quotient Reminder 252 12 1 122 6 0 62 3 0 32 1 1 12 0 1

2510  = 110012

Fractional part

0.62510 = 0.1012

Therefore = 25.62510 = 11001.1012

Conversion of binary to decimal

It is required is to find the decimal value of each binary digit position containing a 1 and add them up.

Example 1 Convert binary (10110)2 into a decimal number.

Solution. The binary number given is 1 0 1 1 02

Positional weights                 4 3 2 1 0

1 × 24 + 0 × 23+ 1 × 22 + 1 × 21 + 0 × 20

= 16 + 0 + 4 + 2 + 0 = (22)10.

Example 2: Convert binary 110112 to decimal number

Solution: Binary number given is:   1 1 0 1 12

Position weights                    4 3 2 1 0

1 x 24 + 1 x 23 + 0 x22  + 1 x 21 + 1 x20

16+ 8 + 0+ 2+ 1 = 2710

Example 3: Convert 1010.0112 into a decimal number.

Solution. The binary number given is         1 0 1 0. 0 1 12

Positional weights                     3 2 1 0 -1-2-3

1 × 23 + 0 × 22 + 1 × 21 + 0 × 20 + 0 × 2-1 + 1 × 2-2 + 1 × 2-3

= 8 + 0 + 2 + 0 + 0 + 0.25 + 0.125

1010.0112  = (10.375)10.

### Conversion of Decimal number to octal number

Repeatedly divide by eight and record the remainder for each division – read “answer” upwards.

Example 1: Rewrite the decimal number 21510  as an octal number.

Solution

 Division Quotient Reminder 2158 26 7 268 3 2 38 0 3

21510 = 3278

Example 2: Convert decimal 179210 to octal number

Solution

 Division Quotient Reminder 17928 224 0 2248 28 0 288 3 4 38 0 3

179210 = 34008

Conversion of octal to decimal

The conversion can also be performed in the conventional mathematical way, by showing each digit place as an increasing power of 8.

Example 1: Convert 3458 to decimal number

Solution

Octal number given is = 345

Position weights        210

3458     = 3 x 82 + 4 x 81 + 5 x  80

= (3 x 64) + (4 x 8 + (5 x 1)

= 192 + 32 +5 = 22910

Example 2: Convert 34628  into a decimal number.

Solution. The octal number given is 3 4 6 28

Positional weights                 3 2 1 0

3 × 83 + 4 × 82 + 6 × 81 + 2 × 80

= 1536 + 256 + 48 + 2= (1842)10

= (1842)10.

Example 3: Convert 362.358 into a decimal number.

Solution. The octal number given is 3 6 2. 3 5

Positional weights                 2 1 0 -1-2

3 × 82 + 6 × 81 + 2 × 80 + 3 × 8-1 + 5 × 8-2

= 192 + 48 + 2 + 0.375 + 0.078125

= (242.453125)10.

DECIMAL AND HEXADECIMAL

Conversion of Decimal Number to Hexadecimal Number

To convert decimal number to hexadecimal, divide the decimal number by 16.

Example 1: Convert 179210  decimal to hexadecimal:

Solution

 Division Quotient Reminder 179216 112 0 11216 7 0 716 0 7

179210 = 70016

Conversion of Hexadecimal-to-decimal

Example1: Convert 42AD16  into a decimal number.

Solution. The hexadecimal number given is 4 2 A D

Positional weights                     3 2 1 0

4 × 163 + 2 × 162 + 10 × 161 + 13 × 160

= 16384 + 512 + 160 + 13

= (17069)10

Example 2:  Convert 42A.1216 into a decimal number.

Solution. The hexadecimal number given is 4 2 A. 1 2

Positional weights                       2 1 0 -1-2

4 × 162+ 2 × 161 + 10 × 160 + 1 × 16-1 + 1 × 16-2

= 1024 + 32 + 10 + 0.0625 + 0.00390625

= (1066.06640625)10.

Conversion of Decimal Number to Hexadecimal Number .

Example: Rewrite the decimal number 21510 as an octal number.

16   215

16    13   R=7

16    0     R =1310  = D

Therefore: 21510  = D716

Computers store information in the form of "1" and "0"s in different types of storages such as memory, hard disk, usb drives etc. The most common digital data storage unit is byte which is 8 bits.

For your information, computer data is expressed as bytes, kilobytes, megabytes as it is in the metric system, but 1 kilobyte is 1024 bytes not 1000 bytes.

Data storage units are: bit, byte, kilobyte (kb), megabyte (mb), gigabyte (gb), terabyte (tb), petabyte

A 'bit' (short for Binary Digit) is the smallest unit of data that can be stored by a computer. Each 'bit' is represented as a binary number, either 1 (true) or 0 (false).

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