Week 2 and 3 – SS1 First Term General Mathematics Notes

 
 Week 2.

NUMBER BASES /BASE NUMBER.

Base number is the basis of which each place value column in a number system or the classification of numbers to which one or more other numbers are appended or added.

TYPES OF BASE NUMBERS.

OCTAL BASE; Octal base are numbers express in base eight. E.g. 25
DENARY/DECIMAL BASE: These are numbers express in base ten. E.g. 18
BINARY: These are numbers express in base two. E.g. 1100
BICIMAL: This is the fractional binary number or fraction in base two. E.g.() =()= 0.10101… in base two.
DUODECIMAL BASE: This is the number system that is express in base 12.
HEXADECIMAL: Is system of numbers which is express in base 16. I.e base 2,3,4,5,6,7,8,9,A,B,C,D,E,F.
HINT: No number must be equal or greater than the base number in operation. If you are working in base two, the highest digit will be 1 and the lowest number is 0

EXPRESSION NUMBERS IN BASE TEN.

450 = 4 × + 5× + 0× in base ten.

CONVERTION OF NUMBERS TO BASE TEN

EXAMPLE;
Convert the following numbers to denary base:
b. c. .
Solution
101111 =1x +0x +1x +1x +1x +1x +1x
=1×64+0x32+1×16+1×8+1×4+1×2+1×1
=64+0+16+8+4+2+1
=9
B. 43 = 4x+ 3x +2x
= 4×25+3×5+2×1
= 100+15+2
=11.
C.. 43 = 4x + 3x +1x
= 4+3X+1

CONVERTION OF BASE NUMBERS FROM BASE TEN TO ANOTHER BASE.

Express the following base ten numbers to each base giving:
a. 1007 to i. octal base ii.Binary base.
b. 761 to ( i).Base 12 (ii). Base16
SOLUTION

1. 100 =8 1007 2 1007
   1. 125 r 7 2 503 r 1

8 15 r 5 2 251 r 1    2 125 r 1
8 0 r 1 2 62 r 1
100= 175 2 31 r 0
2 15 r 1
2 7 r 1
2 3 r 1
2 1 r 1
2 0 r 1
100= 111110111

1. 76= 12 761 16 761

   12 63 r 5 16 47 r 9
   12 5 r 3 16 2 r F
   12 0 r 5 16 0 r 2
   76 = 53 76= 2F
   CONVERTION FROM ONE BASE TO ANOTHER
   HINT: First express the number to base ten and then convert from base ten to the required base.
   EXAMPLE
   Express 31 to octal base
   Solution
   31 = 3 X + 1 X + 3 X
   = 3 X 36 + 1 X 6 + 3 X 1
   =108 +6 +3 = 11
   117 base ten to Octal base8 117
   8 14 r 5
   8 1 r 6
   31= 16
   FRACTIONAL BASE NUMBER
   EXAMPLE: Convert 1011.0 to denary base.
   SOLUTION
   1011.0 = 1 X + 0 X + 1x + 1 X + 0 X + 1 X
   = 1X8 + 0X4 +1X2 + 1X1 +1X +1X
   = 8 + 0 + 2 + 1 + +
   =11 .
   EXAMPLE:
   Express as bicimal number.
   SOLUTION
   (=( .= 0.10101010…
   ASSESSMENT: Students should work the following questions

1. Express the following base numbers to base ten.
   1. 312.2 b. 1051.1 c .2341

2. Convert the following base ten numbers to bicimals:
(a). (b). (c).(d). (e).
3. Convert the following to base; I. Base 5 ii. Base12. iii. Base 15
a. 5 b. 12 c. 1000 d. 12110.

 
  WEEK 3
RULES OF BASE NUMBER

1. Numbers must not be equal to or greater than the base number under consideration.
2. Base numbers of the same base can be added,subtracted, multiplied and divided otherwise it must first be converted to base ten or equal base before the required operation is done.
3. When subtracting base numbers , the number carried from nearby to support the other becomes the base in operation added to the original number in that position.

   BASIC OPERATIONS OF BASE NUMBER.
   EXAMPLE

   1. Find the sum of the octal numbers 174 and 233. (B). Simplify 23121. (c). find the product of 214 and 23 both in base five.(D). if 10= 68, find the value of x?

   SOLUTION
   A 1 7 4 b. 2 3 1 1 C. 2 1 4
   + 2 3 – 2 1 3 x 2
   4 2 2 0 3 1 2 0 2     . + 4 3 3
   1 1 0 3

   1. 10 = 68

      1 X + 0 X + 4 X = 68
      + 0 + 4 = 68

= 68 – 4 : = 64
X = ±
APPLICATION OF BASE NUMBER TO COMPUTER PROGRAMMING
In computer programming the punched cards uses the binary numbers instead of the letters.
A = 1. B = 2. C = 3. D = 4. E = 5. F = 6. P = 16. U =21. Z = 26. The binary equivalent of the number code of letters in binary, such as:
A = 00001, B = 00010, C = 00011, p = 10000, Z = 11010.
Yes = 1 and No = 0
ASSESSMENT: The students are to do the following questions:

1. If 410 = 211 + . Findx?
2. Simplify the following number bases:
   1. 1101x 10 ii. 61 50 iii. If 12 = 83, find y?
3. Represent I LOVE MATHEMATICS in binary code.

ASSIGNMENT: MAN Mathematics for senior secondary schools 1. Page 8, Exercise C4.Numbers,1,2,3 and 7. And miscellaneous Exercises number 3, 6, 10, 14 and 15

 MORAL OBJECTIVE: PSALM 90:12. Teach us to number our days so that we may grow in wisdom.