ITM 207 CH 2 Notes
CHAPTER 2
Number: A unit of an abstract mathematical system subject to the laws of arithmetic
Natural Number: The number 0 and any number obtained by repeatedly adding 1 to it
Examples: 100, 0, 45645, 32
Negative number: A value less than 0, with a sign opposite to its positive counterpart (- sign)
Examples: -24, -1, -45645, -32
Integer: A natural number a negative of a natural number or zero
Examples: 249, 0, - 45645, - 32
Rational Number: An integer or the quotient of 2 integers (division by zero excluded)
Examples: -249, -1, 0, 3/7, -2/5
Base: The foundational value of a number system, which dictates the number of digits and the value of
digit positions
Positional Notation: A system of expressing numbers in which the digits are arranged in succession, the
position of each digit has a place value, and the number is equal to the sum of the products of each digit
1
by its place value
n-1 n-2
As a Formula: d n R + dn-1* R + ... +2d * R + 1
n is the number of digits in the number
d is the digit in the i position in the number
R is the base of the number
Example: 642 is 600 + 40 +2 in BASE 10
2
6 x 10 = 6 x 100 = 600
+ 4 x 10 = 4 x 10 = 40
2
+ 2 x 10º = 2 x 1 = 2 = 642 in base 10 642 is 6 * 10 + 4 * 10 + 2
3 2 1
This number is in
The power
base 10 indicates the
position of the
number
Binary Digit: A digit in the binary number system; a 0 or a 1
Decimal is base 10 and has 10 digits: 0,1,2,3,4,5,6,7,8,9
Binary is base 2 and has 2 digits: 0,1 ITM 207 CH 2 Notes
For a number to exist in a given base, it can only contain the digits in that base, which range
from 0 up to (but not including) the base.
How are digits in bases higher than 10 represented?
With distinct symbols for 10 and above. Base 16 has 16 digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F
What is the decimal Equivalent of the Octal number 642? (Converting Octal to Decimal)
6 x 8 = 6 x 64 = 384
1
+4 x 8 = 4 x 8 = 32
+2 x 8 = 2 x 1 = 2
= 418 in base 10
What is the decimal equivalent of the hexadecimal number DEF? (Converting Hexadecimal to Decimal)
2
D x 16 = 13 x 256 = 3328
1
+ E x 16 = 14 x 16 = 224 *Remember, the digits in base 16 are
+ F x 16º = 15 x 1 = 15 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
= 3567 in base 10
What is the decimal Equivalent of the binary number 1101110? (Converting Binary to Decimal)
6
1 x 2 = 1 x 64 = 64
+ 1 x 2 = 1 x 32 = 32
4
+ 0 x 2 = 0 x 16 = 0
+ 1 x 2 = 1 x 8 = 8
+ 1 x 2 = 1 x 4 = 4
1
+ 1 x 2 = 1 x 2 = 2
+ 0 x 2º = 0 x 1 = 0
=110 in base 10
Arithmetic

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