CSI CHAPTER 2 (BINARY VALUES AND NUMBER SYSTEM)

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

Byte

8 binary digits

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.

Integer

A natural number, a negative of a natural number or zero. Examples: 8,-5, 68, -675

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 1.

Number

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

Negative number

A value less than zero, with a sign opposite to its positive counterpart. Examples: -2, -75, -8

Rational number

An integer or a quotient of two integers, that is, any value that can be expressed as a fraction. Examples: -249, -1, 0, 3/7, -2/5

Decimal Numbers

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.

Octal

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

Hexadecimal

Base that has sixteen digit symbols 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 than 9.

Binary Digit

Binary that has 2 digit symbols 0,1

Base 10

Decimal that has ten-digit symbols 0,1,2,3,4,5,6,7,8,9

Converting Binary to Hexadecimal

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

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.

In computer parlance

One binary digit is called a bit, two digits are called a crumb, four digits are called a nibble, and eight digits are called a byte.

Base

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

Natural Number

The number zero and any number obtained by repeatedly adding one to it. Examples: 2, 58, 953, 0

Hashing

a computing technique that takes numbers and scrambles them.

algorithm

a plan or outline of a solution;a logical sequence of steps that solve a problem.

base

one way to scramble numbers is to interpret them in a different ________.

Bit

single binary digit