{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Números\n",
"\n",
"## Sistemas de Números"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Sistema decimal é o sistema numérico mais utilizado. Mas o computador entende apenas binário. \n",
"\n",
"Os sistemas de números **binários**, **octais** e **hexadecimais** estão intimamente relacionados e podemos exigir a conversão de decimal nesses sistemas. \n",
"\n",
"O sistema decimal é a base 10 (dez símbolos, 0-9, são usados para representar um número) e, da mesma forma: \n",
"\n",
"- binário é a base 2, \n",
"- octal é a base 8 \n",
"- hexadecimal é a base 16.\n",
"\n",
"Um número com o prefixo '0b' é considerado **binário**, '0o' é considerado **octal** e '0x' como **hexadecimal**. \n",
"\n",
"Por exemplo:\n",
"\n",
"- **Decimal** = `112` \n",
"- **Binário** = `0b1110000`\n",
"- **Octal** = `0o160`\n",
"- **Hexadecimal** = `0x70`"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Vamos definir um número decimal para executarmos conversões"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Versão decimal: 8\n",
"Versão binária: 0b1000\n",
"Versão octal: 0o10\n",
"Versão hexadecimal: 0x8\n"
]
}
],
"source": [
"decimal = 8\n",
"\n",
"print(f'Versão decimal: {decimal}')\n",
"print(f'Versão binária: {bin(decimal)}')\n",
"print(f'Versão octal: {oct(decimal)}')\n",
"print(f'Versão hexadecimal: {hex(decimal)}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Utilizando F-Strings para Conversões \n",
"\n",
"Vamos novamente definir um número decimal e fazer conversões"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Decimal: 255.00\n",
"Hexadecimal: ff\n",
"Binário: 11111111\n",
"Octal: 377\n",
"Científico: 2.550000e+02\n"
]
}
],
"source": [
"dec = 255\n",
"\n",
"print(f'Decimal: {dec:.2f}')\n",
"print(f'Hexadecimal: {dec:x}')\n",
"print(f'Binário: {dec:b}')\n",
"print(f'Octal: {dec:o}')\n",
"print(f'Científico: {dec:e}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Manipulação de Binários\n",
"\n",
"Vejamos informações e objetivos relacionados à manipulação de bits em Python (manipulação binária).\n",
"\n",
"Algumas tarefas incluem:\n",
"\n",
"- Transformar \"11011000111101 ...\" em bytes (preenchido à esquerda ou à direita, 0 ou 1) e vice-versa.\n",
"- Intervalos de fatia de bits\n",
"- Gire os bits, endereçados pelo bit. Ou seja, digamos: \"gire os bits 13-17, envolvendo as bordas\" ou \"gire os bits 13-17, perca os bits de um lado, defina todos os novos bits como 0\".\n",
"- Da mesma forma, reverta regiões de bits, aplique lógica a regiões de bits, etc.\n",
"- Alterne Endianness, com diferentes tamanhos de bloco.\n",
"- Aplique operações em agrupamentos de blocos: ex: aplique XOR 10101 (5 bits) repetidamente em um campo.\n",
"\n",
"### Manipulações\n",
"\n",
"#### Binário para Inteiro Decimal"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"33"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"int('00100001', 2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Binário para Hexadecimal"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"ff\n"
]
}
],
"source": [
"print(f'{int(\"11111111\", 2):x}')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1b6\n"
]
}
],
"source": [
"print(f'{int(\"0110110110\", 2):x}')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"7f\n"
]
}
],
"source": [
"print(f'{int(\"01111111\", 2):x}')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Para character (máximo 8 bits)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"';'"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chr(int('111011', 2))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'v'"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chr(int('1110110', 2))"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'w'"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chr(int('1110111', 2))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'~'"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chr(int('01111110', 2))"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'?'"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chr(int('111111', 2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Character para inteiros"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"254"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"int('11111110', 2)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'þ'"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chr(int('11111110', 2))"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"254"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ord('þ')"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"112"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"ord('p')"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'p'"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chr(int('1110000', 2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Bits Individuais"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 << 0"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 << 1"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 << 2"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 << 3"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"16"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 << 4"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"256"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 << 8"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### String Hex para Inteiro Decimal"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"255"
]
},
"execution_count": 39,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"int('0xff', 16)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"16"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"int('0x10', 16)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### String Oct para Inteiro Decimal"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"112"
]
},
"execution_count": 98,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"int('0o160', 8)"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"31"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"int('0o037', 8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Inteiro para String Binária"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [],
"source": [
"def bin(s):\n",
" return str(s) if s<=1 else bin(s>>1) + str(s&1)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'11'"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bin(3)"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'1000110'"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bin(70)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'11111111'"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bin(255)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Tabela de Números"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [],
"source": [
"from prettytable import PrettyTable"
]
},
{
"cell_type": "code",
"execution_count": 115,
"metadata": {},
"outputs": [],
"source": [
"tabela = PrettyTable()"
]
},
{
"cell_type": "code",
"execution_count": 116,
"metadata": {},
"outputs": [],
"source": [
"tabela.field_names = [\"Decimal\", \"Hexadecimal\", \"Octal\", \"Binário\"]"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {},
"outputs": [],
"source": [
"for n in range(128):\n",
" tabela.add_row([n, hex(n), oct(n), bin(n)])"
]
},
{
"cell_type": "code",
"execution_count": 118,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"+---------+-------------+-------+---------+\n",
"| Decimal | Hexadecimal | Octal | Binário |\n",
"+---------+-------------+-------+---------+\n",
"| 0 | 0x0 | 0o0 | 0 |\n",
"| 1 | 0x1 | 0o1 | 1 |\n",
"| 2 | 0x2 | 0o2 | 10 |\n",
"| 3 | 0x3 | 0o3 | 11 |\n",
"| 4 | 0x4 | 0o4 | 100 |\n",
"| 5 | 0x5 | 0o5 | 101 |\n",
"| 6 | 0x6 | 0o6 | 110 |\n",
"| 7 | 0x7 | 0o7 | 111 |\n",
"| 8 | 0x8 | 0o10 | 1000 |\n",
"| 9 | 0x9 | 0o11 | 1001 |\n",
"| 10 | 0xa | 0o12 | 1010 |\n",
"| 11 | 0xb | 0o13 | 1011 |\n",
"| 12 | 0xc | 0o14 | 1100 |\n",
"| 13 | 0xd | 0o15 | 1101 |\n",
"| 14 | 0xe | 0o16 | 1110 |\n",
"| 15 | 0xf | 0o17 | 1111 |\n",
"| 16 | 0x10 | 0o20 | 10000 |\n",
"| 17 | 0x11 | 0o21 | 10001 |\n",
"| 18 | 0x12 | 0o22 | 10010 |\n",
"| 19 | 0x13 | 0o23 | 10011 |\n",
"| 20 | 0x14 | 0o24 | 10100 |\n",
"| 21 | 0x15 | 0o25 | 10101 |\n",
"| 22 | 0x16 | 0o26 | 10110 |\n",
"| 23 | 0x17 | 0o27 | 10111 |\n",
"| 24 | 0x18 | 0o30 | 11000 |\n",
"| 25 | 0x19 | 0o31 | 11001 |\n",
"| 26 | 0x1a | 0o32 | 11010 |\n",
"| 27 | 0x1b | 0o33 | 11011 |\n",
"| 28 | 0x1c | 0o34 | 11100 |\n",
"| 29 | 0x1d | 0o35 | 11101 |\n",
"| 30 | 0x1e | 0o36 | 11110 |\n",
"| 31 | 0x1f | 0o37 | 11111 |\n",
"| 32 | 0x20 | 0o40 | 100000 |\n",
"| 33 | 0x21 | 0o41 | 100001 |\n",
"| 34 | 0x22 | 0o42 | 100010 |\n",
"| 35 | 0x23 | 0o43 | 100011 |\n",
"| 36 | 0x24 | 0o44 | 100100 |\n",
"| 37 | 0x25 | 0o45 | 100101 |\n",
"| 38 | 0x26 | 0o46 | 100110 |\n",
"| 39 | 0x27 | 0o47 | 100111 |\n",
"| 40 | 0x28 | 0o50 | 101000 |\n",
"| 41 | 0x29 | 0o51 | 101001 |\n",
"| 42 | 0x2a | 0o52 | 101010 |\n",
"| 43 | 0x2b | 0o53 | 101011 |\n",
"| 44 | 0x2c | 0o54 | 101100 |\n",
"| 45 | 0x2d | 0o55 | 101101 |\n",
"| 46 | 0x2e | 0o56 | 101110 |\n",
"| 47 | 0x2f | 0o57 | 101111 |\n",
"| 48 | 0x30 | 0o60 | 110000 |\n",
"| 49 | 0x31 | 0o61 | 110001 |\n",
"| 50 | 0x32 | 0o62 | 110010 |\n",
"| 51 | 0x33 | 0o63 | 110011 |\n",
"| 52 | 0x34 | 0o64 | 110100 |\n",
"| 53 | 0x35 | 0o65 | 110101 |\n",
"| 54 | 0x36 | 0o66 | 110110 |\n",
"| 55 | 0x37 | 0o67 | 110111 |\n",
"| 56 | 0x38 | 0o70 | 111000 |\n",
"| 57 | 0x39 | 0o71 | 111001 |\n",
"| 58 | 0x3a | 0o72 | 111010 |\n",
"| 59 | 0x3b | 0o73 | 111011 |\n",
"| 60 | 0x3c | 0o74 | 111100 |\n",
"| 61 | 0x3d | 0o75 | 111101 |\n",
"| 62 | 0x3e | 0o76 | 111110 |\n",
"| 63 | 0x3f | 0o77 | 111111 |\n",
"| 64 | 0x40 | 0o100 | 1000000 |\n",
"| 65 | 0x41 | 0o101 | 1000001 |\n",
"| 66 | 0x42 | 0o102 | 1000010 |\n",
"| 67 | 0x43 | 0o103 | 1000011 |\n",
"| 68 | 0x44 | 0o104 | 1000100 |\n",
"| 69 | 0x45 | 0o105 | 1000101 |\n",
"| 70 | 0x46 | 0o106 | 1000110 |\n",
"| 71 | 0x47 | 0o107 | 1000111 |\n",
"| 72 | 0x48 | 0o110 | 1001000 |\n",
"| 73 | 0x49 | 0o111 | 1001001 |\n",
"| 74 | 0x4a | 0o112 | 1001010 |\n",
"| 75 | 0x4b | 0o113 | 1001011 |\n",
"| 76 | 0x4c | 0o114 | 1001100 |\n",
"| 77 | 0x4d | 0o115 | 1001101 |\n",
"| 78 | 0x4e | 0o116 | 1001110 |\n",
"| 79 | 0x4f | 0o117 | 1001111 |\n",
"| 80 | 0x50 | 0o120 | 1010000 |\n",
"| 81 | 0x51 | 0o121 | 1010001 |\n",
"| 82 | 0x52 | 0o122 | 1010010 |\n",
"| 83 | 0x53 | 0o123 | 1010011 |\n",
"| 84 | 0x54 | 0o124 | 1010100 |\n",
"| 85 | 0x55 | 0o125 | 1010101 |\n",
"| 86 | 0x56 | 0o126 | 1010110 |\n",
"| 87 | 0x57 | 0o127 | 1010111 |\n",
"| 88 | 0x58 | 0o130 | 1011000 |\n",
"| 89 | 0x59 | 0o131 | 1011001 |\n",
"| 90 | 0x5a | 0o132 | 1011010 |\n",
"| 91 | 0x5b | 0o133 | 1011011 |\n",
"| 92 | 0x5c | 0o134 | 1011100 |\n",
"| 93 | 0x5d | 0o135 | 1011101 |\n",
"| 94 | 0x5e | 0o136 | 1011110 |\n",
"| 95 | 0x5f | 0o137 | 1011111 |\n",
"| 96 | 0x60 | 0o140 | 1100000 |\n",
"| 97 | 0x61 | 0o141 | 1100001 |\n",
"| 98 | 0x62 | 0o142 | 1100010 |\n",
"| 99 | 0x63 | 0o143 | 1100011 |\n",
"| 100 | 0x64 | 0o144 | 1100100 |\n",
"| 101 | 0x65 | 0o145 | 1100101 |\n",
"| 102 | 0x66 | 0o146 | 1100110 |\n",
"| 103 | 0x67 | 0o147 | 1100111 |\n",
"| 104 | 0x68 | 0o150 | 1101000 |\n",
"| 105 | 0x69 | 0o151 | 1101001 |\n",
"| 106 | 0x6a | 0o152 | 1101010 |\n",
"| 107 | 0x6b | 0o153 | 1101011 |\n",
"| 108 | 0x6c | 0o154 | 1101100 |\n",
"| 109 | 0x6d | 0o155 | 1101101 |\n",
"| 110 | 0x6e | 0o156 | 1101110 |\n",
"| 111 | 0x6f | 0o157 | 1101111 |\n",
"| 112 | 0x70 | 0o160 | 1110000 |\n",
"| 113 | 0x71 | 0o161 | 1110001 |\n",
"| 114 | 0x72 | 0o162 | 1110010 |\n",
"| 115 | 0x73 | 0o163 | 1110011 |\n",
"| 116 | 0x74 | 0o164 | 1110100 |\n",
"| 117 | 0x75 | 0o165 | 1110101 |\n",
"| 118 | 0x76 | 0o166 | 1110110 |\n",
"| 119 | 0x77 | 0o167 | 1110111 |\n",
"| 120 | 0x78 | 0o170 | 1111000 |\n",
"| 121 | 0x79 | 0o171 | 1111001 |\n",
"| 122 | 0x7a | 0o172 | 1111010 |\n",
"| 123 | 0x7b | 0o173 | 1111011 |\n",
"| 124 | 0x7c | 0o174 | 1111100 |\n",
"| 125 | 0x7d | 0o175 | 1111101 |\n",
"| 126 | 0x7e | 0o176 | 1111110 |\n",
"| 127 | 0x7f | 0o177 | 1111111 |\n",
"+---------+-------------+-------+---------+\n"
]
}
],
"source": [
"print(tabela)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}