Decimal

Decimal is a base-10 number system that uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is the most commonly used number system in everyday life. In the decimal system, each digit represents powers of 10.

Each digit takes up 3.32 bits.

Conversion

Converting to decimal from other bases involves multiplying each digit by the base raised to the power of its position and then summing the results.

From Binary

The rough logic for converting a binary number to decimal is as follows:

$$\begin{array}{rl}\text{Let }b& =\text{the binary number to convert}\\ \text{Let }\text{decimal}& =0\\ \text{For }i& =0\text{ to }\text{length of }b-1\\ \text{decimal}& +={\mathrm{b}}_{\mathrm{i}}\times 2^i\\ \text{Return }\text{decimal}\end{array}$$

python

def binary_to_decimal(binary: str) -> int:
    decimal = 0
    binary = binary[::-1]
    for i in range(len(binary)):
        decimal += int(binary[i]) * (2 ** i)
    return decimal

print(binary_to_decimal("1010"))  # 10

js

function binaryToDecimal(binary) {
    let decimal = 0;
    binary = binary.split("").reverse().join("");
    for (let i = 0; i < binary.length; i++) {
        decimal += parseInt(binary[i]) * Math.pow(2, i);
    }
    return decimal;
}

console.log(binaryToDecimal("1010")); // 10

cpp

#include <iostream>
#include <cmath>
using namespace std;

int binaryToDecimal(string binary) {
    int decimal = 0;
    reverse(binary.begin(), binary.end());
    for (int i = 0; i < binary.length(); i++) {
        decimal += (binary[i] - '0') * pow(2, i);
    }
    return decimal;
}

int main() {
    cout << binaryToDecimal("1010") << endl; // 10
}

rust

fn binary_to_decimal(binary: &str) -> i32 {
    let mut decimal = 0;
    let reversed_binary: String = binary.chars().rev().collect();
    for (i, digit) in reversed_binary.chars().enumerate() {
        if digit == '1' {
            decimal += 2i32.pow(i as u32);
        }
    }
    decimal
}

fn main() {
    println!("{}", binary_to_decimal("1010")); // 10
}

From Octal

$$\begin{array}{rl}\text{Let }o& =\text{the octal number to convert}\\ \text{Let }\text{decimal}& =0\\ \text{For }i& =0\text{ to }\text{length of }o-1\\ \text{decimal}& +={\mathrm{o}}_{\mathrm{i}}\times 8^i\\ \text{Return }\text{decimal}\end{array}$$

python

def octal_to_decimal(octal: str) -> int:
    decimal = 0
    octal = octal[::-1]
    for i in range(len(octal)):
        decimal += int(octal[i]) * (8 ** i)
    return decimal

print(octal_to_decimal("24"))  # 20

js

function octalToDecimal(octal) {
    let decimal = 0;
    octal = octal.split("").reverse().join("");
    for (let i = 0; i < octal.length; i++) {
        decimal += parseInt(octal[i]) * Math.pow(8, i);
    }
    return decimal;
}

console.log(octalToDecimal("24")); // 20

cpp

#include <iostream>
#include <cmath>
using namespace std;

int octalToDecimal(string octal) {
    int decimal = 0;
    reverse(octal.begin(), octal.end());
    for (int i = 0; i < octal.length(); i++) {
        decimal += (octal[i] - '0') * pow(8, i);
    }
    return decimal;
}

int main() {
    cout << octalToDecimal("24") << endl; // 20
}

rust

fn octal_to_decimal(octal: &str) -> i32 {
    let mut decimal = 0;
    let reversed_octal: String = octal.chars().rev().collect();
    for (i, digit) in reversed_octal.chars().enumerate() {
        decimal += (digit.to_digit(10).unwrap() as i32) * 8i32.pow(i as u32);
    }
    decimal
}

fn main() {
    println!("{}", octal_to_decimal("24")); // 20
}

From Hexadecimal

$$\begin{array}{rl}\text{Let }h& =\text{the hexadecimal number to convert}\\ \text{Let }\text{decimal}& =0\\ \text{For }i& =0\text{ to }\text{length of }h-1\\ \text{If }{\mathrm{h}}_{\mathrm{i}}& \text{ is a digit}\\ \text{decimal}& +={\mathrm{h}}_{\mathrm{i}}\times {16}^i\\ \text{Else}\\ \text{decimal}& +=({\mathrm{h}}_{\mathrm{i}}-55)\times {16}^i\\ \text{Return }\text{decimal}\end{array}$$

python

def hexadecimal_to_decimal(hexadecimal: str) -> int:
		decimal = 0
		hexadecimal = hexadecimal[::-1]
		for i in range(len(hexadecimal)):
				if hexadecimal[i].isdigit():
						decimal += int(hexadecimal[i]) * (16 ** i)
				else:
						decimal += (ord(hexadecimal[i].upper()) - 55) * (16 ** i)
		return decimal

print(hexadecimal_to_decimal("A"))  # 10

js

function hexadecimalToDecimal(hexadecimal) {
		let decimal = 0;
		hexadecimal = hexadecimal.split("").reverse().join("");
		for (let i = 0; i < hexadecimal.length; i++) {
				if (hexadecimal[i].match(/[0-9]/)) {
						decimal += parseInt(hexadecimal[i]) * Math.pow(16, i);
				} else {
						decimal += (hexadecimal[i].toUpperCase().charCodeAt(0) - 55) * Math.pow(16, i);
				}
		}
		return decimal;
}

console.log(hexadecimalToDecimal("A")); // 10

cpp

#include <iostream>
#include <cmath>
using namespace std;

int hexadecimalToDecimal(string hexadecimal) {
		int decimal = 0;
		reverse(hexadecimal.begin(), hexadecimal.end());
		for (int i = 0; i < hexadecimal.length(); i++) {
				if (isdigit(hexadecimal[i])) {
						decimal += (hexadecimal[i] - '0') * pow(16, i);
				} else {
						decimal += (toupper(hexadecimal[i]) - 55) * pow(16, i);
				}
		}
		return decimal;
}

int main() {
		cout << hexadecimalToDecimal("A") << endl; // 10
}

rust

fn hexadecimal_to_decimal(hexadecimal: &str) -> i32 {
		let mut decimal = 0;
		let reversed_hexadecimal: String = hexadecimal.chars().rev().collect();
		for (i, digit) in reversed_hexadecimal.chars().enumerate() {
				if digit.is_digit(10) {
						decimal += digit.to_digit(10).unwrap() as i32 * 16i32.pow(i as u32);
				} else {
						decimal += (digit.to_ascii_uppercase() as u8 - 55) as i32 * 16i32.pow(i as u32);
				}
		}
		decimal
}

fn main() {
		println!("{}", hexadecimal_to_decimal("A")); // 10
}