Number Base System

Number Base System JSS 2


Number Base System

A number base system is the collection of symbols and rules for representing both small and large numbers. There are many number systems used today, some are examined below.


Types of Number Base Systems

Binary Number System

The Binary Number System is the number system in base 2. There are only two symbols (digits) in this system, which are 0 and 1.

Octal Number System

Octal or Oct means eight (8). Hence, the Octal Number System is a number system in base 8. There are eight (8) symbols used in this system: 0, 1, 2, 3, 4, 5, 6, and 7.

Decimal or Denary Number System

Decimal Number System is base ten (10). Ten symbols are used in this system: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. This is the system we use for everyday counting.

Hexadecimal Number system

Hex and decimal represent 6 and 10 respectively, making the Hexadecimal Number System a base 16 system. The sixteen symbols used are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. It is important to note that letters A, B, C, D, E and F represent the decimal values of 10, 11, 12, 13, 14 and 15 respectively.


Conversion From One Number Base System To Another

Binary to Decimal Number Conversion

To convert from binary to Decimal, multiply each binary digit by an increasing power (right to left) of 2 and sum the results.

Example 1: Convert 11011012 to a decimal number.
Solution
11011012
= (1×26)+(1×25)+(0×24)+(1×23)+(1×22)+(0×21)+(1×20)

= 1×64+1×32+0×16+1×8+1×4+0×2+1×1
= 64+32+0+8+4+0+1
= 109
Therefore, 11011012 = 10910
Example 2: Convert 101110011.11012 to decimal.
Solution
101110011.11012
= 1×28+0×27+1×26+1×25+1×24+0×23+0×22+1×21+1×20+1×2-1+1×2-2+0×2-3+1×2-4
= 1×256+0×128+1×64+1×32+1×16+0×8+0×4+1×2+1×1+1×&frac{1}{2}+1×&frac{1}{4}+0×&frac{1}{8}+1×&frac{1}{16}
= 256+0+64+32+16+0+0+2+1+0.5+0.25+0+0.0625
= 371 + 0.8125
= 371.8125
Therefore, 101110011.11012 = 371.812510

Conversion from Decimal System to Binary System

To convert from decimal to binary, repeatedly divide the decimal number by two (2) and write down the remainder. The binary result is the remainders read from bottom to top.

Example 1: Convert 10910 to binary.
Solution
2DecRemainder
21091
2540
2271
2131
260
231
211
01

Picking the remainder from bottom to top: 1101101

Therefore, 10910 = 11011012

Conversion from Octal Base System to Decimal Base System

To convert from octal to decimal, multiply each digit by an increasing power (right to left) of eight (8) and sum the result.

Example 1: Convert 34568 to base ten.
Solution
34568
= (3×83) + (4×82) + (5×81) + (6×80)
= (3×512) + (4×64) + (5×8) + (6×1)
= 1536 + 256 + 40 + 6
= 1838
Therefore, 34568 = 183810

Conversion from Decimal to Octal Base System

To convert from decimal to octal, repeatedly divide the decimal number by eight (8) and write down the remainder.

Example 1: Convert 183810 to Octal.
Solution
8DecRemainder
818386
82295
8284
833
03

Picking the remainder from bottom to top: 3456

Therefore, 183810 = 34568

Conversion from Hexadecimal base System to Decimal Base System

To convert from hexadecimal to decimal, multiply each digit by an increasing power (right to left) of sixteen (16) and sum the result.

Example 1: Convert 89F16 to decimal.
Solution
89F16
= (8×162) + (9×161) + (F×160)

= (8×256) + (9×16) + (15×1)
= 2048 + 144 + 15
= 2207
Therefore, 89F16 = 220710
Example 2: Convert CAFE16 to decimal.
Solution
CAFE16
= (C×163) + (A×162) + (F×161) + (E×160)

= (12×4096) + (10×256) + (15×16) + (14×1)
= 49152 + 2560 + 240 + 14
= 51966
Therefore, CAFE16 = 5196610

Conversion from Decimal Base System to Hexadecimal Base System

To convert from decimal to hexadecimal, repeatedly divide the decimal number by sixteen (16) and write down the remainder.

Example 1: Convert 4780610 to Hexadecimal.
Solution
16DecRemainderRemainder in Hex
164780614E
16298711B
1618610A
161111B
0

Picking Remainder in Hex from bottom to top: BABE

Therefore, 4780610 = BABE16

Click here for an extensive coverage on number base system


🧠 Test Your Knowledge 📝

See how much you've learned about Number Base Systems!

1. What is the base of the Hexadecimal Number System?

2. Which decimal value is represented by the hexadecimal symbol 'A'?

3. What is the binary equivalent of the decimal number 510?

4. How many unique symbols (digits) are used in the Octal Number System?

Comments

  1. I goggled key basic statement for jss2 I don't understand

    ReplyDelete
  2. Write a basic code of A-2

    ReplyDelete
    Replies
    1. You can can use a simple PRINT statement
      E.g
      CLS
      REM program to display letter A -Z
      PRINT "A"
      PRINT "B"



      complete to Z and end the program

      Delete
    2. You can also use the program below
      10 REM this program is written to display letters from A to Z
      20 FOR I = 65 TO 90
      30 PRINT CHR$(I);
      40 NEXT I
      50 END

      Delete
  3. Please Sir, don't really know how to calculate this = (1×26²)+(1×25²) =

    ReplyDelete
    Replies
    1. (1×26²)+(1×25²) = (1×26×26 )+(1×25×25 )
      = (676 )+(625 )
      =1,301

      Delete
  4. I appreciate how it breaks down the concept of different base systems, like binary and decimal, and explains their practical applications, particularly in computing. The examples used make the content relatable and easy to understand. As someone interested in math concepts, I found the step-by-step approach to converting between bases especially helpful. This is a great resource for students looking to strengthen their understanding of number systems. I look forward to reading more educational posts like this.

    ReplyDelete
  5. I love this website

    ReplyDelete

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