Octal numbers use base-8, while binary numbers use base-2. Converting octal numbers to binary is useful in programming for compact representations of binary data and low-level system tasks. In this article, we will write a C program to convert an octal number into its binary equivalent.
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Understanding The Problem
Each octal digit corresponds exactly to three binary digits. To convert octal to binary, each digit is separately converted to its 3-bit binary equivalent, and these groups are combined to form the full binary number. For example, octal 57 converts to binary 101111.
Program 1: Using Arithmetic Method
In this approach, we first convert the octal number into decimal, and then convert the decimal number into binary.
#include <stdio.h>
#include <math.h>
int main() {
int octal, decimal = 0, i = 0, rem;
long long binary = 0, factor = 1;
printf("Enter an octal number: ");
scanf("%o", &octal); // %o reads octal input
// Convert octal to decimal
int temp = octal;
while (temp > 0) {
rem = temp % 10;
decimal += rem * pow(8, i);
temp /= 10;
i++;
}
// Convert decimal to binary
temp = decimal;
while (temp > 0) {
rem = temp % 2;
binary += rem * factor;
temp /= 2;
factor *= 10;
}
printf("Binary equivalent: %lld\n", binary);
return 0;
}This method first converts octal to decimal using powers of 8, then converts decimal to binary by repeatedly dividing by 2 and forming the binary number.
Program 2: Using Strings
This method treats the octal input as a string and converts each digit into a 3-bit binary group, avoiding decimal conversion and handling large numbers safely.
#include <stdio.h>
#include <string.h>
int main() {
char octal[20];
int i;
printf("Enter an octal number: ");
scanf("%s", octal);
printf("Binary equivalent: ");
for (i = 0; i < strlen(octal); i++) {
switch (octal[i]) {
case '0': printf("000"); break;
case '1': printf("001"); break;
case '2': printf("010"); break;
case '3': printf("011"); break;
case '4': printf("100"); break;
case '5': printf("101"); break;
case '6': printf("110"); break;
case '7': printf("111"); break;
default: printf("Invalid octal digit"); return 1;
}
}
printf("\n");
return 0;
}This string-based method directly maps each octal digit to its binary equivalent, making it simple and safe for large inputs.
Program 3: Using sprintf() and Decimal Conversion
We can also use sprintf() to convert the decimal equivalent of the octal number into binary.
#include <stdio.h>
#include <math.h>
int main() {
int octal, decimal = 0, i = 0, rem;
char binary[64];
printf("Enter an octal number: ");
scanf("%o", &octal); // Read octal input
// Convert octal to decimal
int temp = octal;
while (temp > 0) {
rem = temp % 10;
decimal += rem * pow(8, i);
temp /= 10;
i++;
}
// Convert decimal to binary string using sprintf
sprintf(binary, "%b", decimal); // C23 feature: %b prints binary
printf("Binary equivalent: %s\n", binary);
return 0;
}This approach is concise and leverages C23’s %b format specifier for binary output, avoiding manual calculations.
Program 4: Using sscanf()
This method reads the octal input as a string, converts it to decimal using sscanf(), and then prints the binary equivalent using %b.
#include <stdio.h>
int main() {
char octalStr[20];
unsigned int decimal;
printf("Enter an octal number: ");
scanf("%s", octalStr);
// Convert octal string to decimal using sscanf and %o
sscanf(octalStr, "%o", &decimal);
// Print binary using %b (C23)
printf("Binary equivalent: %b\n", decimal);
return 0;
}In this program, sscanf() reads the octal string and automatically converts it into a decimal integer. Then %b in printf() outputs the number in binary. This method is concise, safe for large inputs, and avoids manual calculations.
Program 5: Using strtol()
The strtol() function can convert an octal string directly into a decimal integer, which can then be printed in binary using C23’s %b specifier. This approach is concise, safe for large numbers, and avoids manual arithmetic.
#include <stdio.h>
#include <stdlib.h>
int main() {
char octalStr[20], binary[65];
unsigned long decimal;
printf("Enter an octal number: ");
scanf("%s", octalStr);
// Convert octal string to decimal using strtol with base 8
decimal = strtol(octalStr, NULL, 8);
// Convert decimal to binary string using C23 %b
sprintf(binary, "%b", decimal);
printf("Binary equivalent: %s\n", binary);
return 0;
}This program reads the octal input as a string, converts it to decimal using strtol() with base 8, and then formats it as a binary string using sprintf(). It is concise, modern, and safe for large inputs.
FAQs
Q1: Can this program handle large octal numbers?
Yes, the string-based and sprintf() methods can handle very large numbers, while the arithmetic method may overflow for extremely long inputs.
Q2: Why does each octal digit map to three binary digits?
Because $2^3 = 8$, each octal digit corresponds exactly to a 3-bit binary number.
Q3: Which method is easiest for beginners?
The string-based mapping is simplest, while sprintf() is very concise but requires a C23-compliant compiler.
Conclusion
Converting octal numbers to binary is straightforward when each digit is mapped to its 3-bit binary equivalent. Arithmetic, string-based, and sprintf() methods all provide reliable results. Understanding this conversion is useful for programming, low-level operations, and working with number systems.
References & Additional Resources
- C Programming Tutorial – Covers loops, strings, and conversions in C.
- GeeksforGeeks – Octal to Binary – Examples of multiple conversion methods.
- TutorialsPoint – Number Systems – Complete guide to binary, octal, decimal, and hexadecimal.
