Binary Values and Number Systems

Adding Binary

1+0= 1 0+1= 1 1+1= 0 with a carry of 1 1+1+1= 1 with a carry of 1

Binary Digit

A digit in the binary number system; a 0 or a 1.

Word

A group of one or more bytes; the number of bits in a word is the word length of the computer.

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 by its place value.

Number

A unit of an actual abstract mathematical system subject to the laws of arithmetic.

negative numbers

A value less than 0, with a sign opposite to it's counterpart.

Rational Number

Are either integers or numbers that can be expressed as quotients of two integers.

Octal

Base 8, uses 8 digits which are 0,1,2,3,4,5,6,7, and 8.

Binary

Binary are base 2 numbers, which only use two digits which are o and 1.

Bit

Binary digit

Decimal Numbers

Decimal number are represented using 10 digits, those are 0,1,2,3,4,5,6,7,8, and 9. Therefore the number 79 can be represented in the base 10.

Byte

Eight binary digits

Converting Binary to Hexadecimal

Group the binary digits in groups of 4 starting from the right to the left then convert each to their hexadecimal value. Example 100 1111 0011 is 4F3

Hexadecimal

Hexadecimal is in base 16 and uses 16 digits which are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E, and F. The letters represent the digits of base value higher then 9.

Subtracting Binary

In binary when borrowing we borrow a 2 not a 10. 1-0= 1 1-1=0 0-1= requires a borrow of 2.

Intergers

Include natural numbers, and their negative counterparts.

Real Numbers

Include the natural, integer, and rational categories as well as number thats cannot be expressed as a quotient of two integers (irrational).

Base

The foundational value of a number system, which dictates the number of digits and the value of digit positions.

Natural Number

The number 0 and any number obtained by repeatedly adding 1 to it.