程序代写代做代考 CSE 295 Lecture 1 – Binary

CSE 295 Lecture 1 – Binary
Base Representation
A numeral represents a number using a series of digits in a particular base. Each digit is one of a fixed set of symbols that represent values between 0 and base 􏰀 1. We are taught to think in base 10 (decimal, which uses the ten symbols 0 through 9). We number the digit positions from the right, starting with 0. In decimal, the value of the digit 𝑑 in position 𝑖 in base 𝑏 is 𝒅 􏰁 𝒃𝒊.
digit position → 2 1 0
digitsymbol→ 𝟑 𝟓 𝟏􏰂􏰃 􏰄 3􏰁10􏰅 􏰆5􏰁10􏰂 􏰆1􏰁10􏰃
In these examples, the subscript on the numeral indicates the base (no subscript means base 10): 1011􏰅 􏰄2􏰇 􏰆2􏰂 􏰆2􏰃 􏰄11􏰄1􏰁3􏰅 􏰆2􏰁3􏰃 􏰄12􏰇
􏰀1234􏰈 􏰄 􏰀􏰉1􏰁5􏰇 􏰆2􏰁5􏰅 􏰆3􏰁5􏰂 􏰆4􏰁5􏰃􏰊 􏰄 􏰀194
Binary
Computers use base 2 (binary). Each binary digit is called a bit. Collections of bits can be easily grouped and converted into other bases that are powers of two. The most common grouping is four bits (base 2􏰋 = base 16, which is called hexadecimal or hex). In order to get to 16 symbols, we incorporate the first six letter of the alphabet, which can be equivalently written in upper or lowercase.
These are the most common bases that we will use in this class: 2, 10, and 16. We differentiate between these bases by adding the prefix ‘0b’ for binary and ‘0x’ for hexadecimal; there is no prefix for decimal. The table on the right shows the equivalent numerals for the numbers 0 through 15 in these three major number bases.
Note: We’re still in the realm of pure math here, so the negative sign sits separately from the number and does its own thing. All numbers can be assumed to have an infinite number of leading zeros, which would appear to the left of all shown digits but add no value.
Binary
Decimal
Hex
0b0000
0
0x0
0b0001
1
0x1
0b0010
2
0x2
0b0011
3
0x3
0b0100
4
0x4
0b0101
5
0x5
0b0110
6
0x6
0b0111
7
0x7
0b1000
8
0x8
0b1001
9
0x9
0b1010
10
0xA
0b1011
11
0xB
0b1100
12
0xC
0b1101
13
0xD
0b1110
14
0xE
0b1111
15
0xF
Note: In C, literals (i.e. constants) are expressed in decimal by default. You can use the appropriate prefix to express literals in binary or hexadecimal instead.
However, you should NOT use binary constants in Lab 1a or Lab 1b.