Number Systems

Numbers by themselves are just:

Numbers

What only matters to computers

Binary

8 bit byte

2⁸=256

Signed integer

• can present both positive and negative integers

• 0 means positive

• 1 means negative

• default type in programming

Range for n-bit integer

-(2^n-1) to (2^n-1 -1)

Unsigned Integer

• only represent positive numbers (includes zero)

Range for unsigned Integers

0 to (2^n-1)

What happens when you have too many for the data type

It doesn’t matter, data type must hold more than enough

What is overflow in C

Undefined

Signed vs Unsigned

compares the binary values

Which programming languages do not have unsigned integeres

C# and Java

Bits and bit width

• 8 bit = 2⁸ = 256 (unsigned)

• 16 bit = 216 = 65,536 (width 32,767 to −32,768)

• 32-bit long = 2³²

• 64-bit long long = 2⁶⁴

C language implementation varies by

complier and platform

In binary system, what value is between 0 and 1

Every fractional value aka a float and double

Bit

• Binary Digit

• unambiguous unit used to encode a message for transmission

Byte

• 8 bits

• the smallest unit of data

0 - 1 for storage of a value

in a bit

Float

• single precision floating point

• precision: 24 bits left & right of decimal

• precision limit: 2^24'

• ^{accuracy: 6 decimals}

Double

• double precision floating-point

• precision: 53 bits left & right of decimal

• precision limit: 9 quadrillion

• accuracy: 15 decimals

Number system

• the information stored and processed inside a computer system is represented in machine language which is only 0s and 1s

• writing system for expressing numbers

• mathematical notation for representing numbers of a given set

• also referred to as “a numeral system” or “system of numeration”

What does computer translates all input into

letters, words, special characters to numbers.

humans use “decimal number, computer understands?

“binary” number system that has only 2 (0 and 1) digits

To represent binary numbers concisely we use

Hexadecimal number system, uses 10 digits (0-9) and 6 symbols (A-F)

Value of a digit in a number is determined by

• the digit itself

• the position of the digit

• the base of the number system

Decimal Number System

• human preferred

• it has base 10 as it uses 10 digits (0-9)

• each successive position represents a specific power of base 10

Binary number system

• the one that a computer or a machine understand

• only uses two digits; 0 and 1; base is 2

• just like decimal, value of digits increase from right to left, each successive position represents a specific power of base ( 2 in this case)

All data transfer, storage, and processing done by a

microcomputer is performed digitally using binary codes

Binary system translates every character entered in the computer as a set of

1s and 0s

A single binary digit is called a

bit

A collection of 8 bits is called a

byte

one bite can represent any of

256 characters ; 2⁸ = 256

memory size is referred to in

units of bytes

How to convert from Decimal to Binary and vice versa

Decimal to Binary: Divide by 2, record remainders, read bottom to top.

Binary to Decimal: Assign powers of 2, multiply, and add.

How many digits does hexadecimal use

16 digits: 0 to 9 and A to F; letters A - F represents digits start from 10.

HTML color representations uses

Hex codes of RGB

00 and FF intensity

00 is lowest ; FF is highest

what is the hex code for white and black

FFFFFF: white ; 00000: black

In binary logic and computing 0 and 1 are considered:

0 is False

1 is True