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UNIT 01 · Simple numeric problems

Binary equivalent from 0 to 255

EXERCISE 01DC173 sample runs

THE SYLLABUS QUESTION

What you need to solve

Write a program that shows the binary equivalent of a given positive number between 0 to 255.
Input format & conventions

One integer in the inclusive range 0–255. Zero is supported because it is explicitly included in the syllabus range.

UNDERSTAND THE IDEA

Explanation

Eight bits can represent all integers from 0 through 255. Read each bit from position 7 down to position 0.

Right-shifting moves the selected bit to the least-significant position; bitwise AND with 1 isolates it. Leading zeros make the eight-bit representation clear.

PLAN BEFORE CODING

Algorithm

  1. Read and validate the decimal value.
  2. Visit bit positions 7 down to 0.
  3. Use (value >> bit) & 1 to extract each bit.
  4. Print eight bits and a newline.

SEE THE CONTROL FLOW

Flowchart

Follow the arrows from Start. Diamonds ask a question; labeled arrows show the answer. A returning arrow repeats a loop. Function internals are grouped where needed; later input checks follow the rules in the program.

Flowchart for Binary equivalent from 0 to 255: input, decisions, processing, output and loop paths

On a phone, scroll sideways to read the diagram at full size. Open full-size flowchart ↗

C17

Complete C program

Download .c
#include <stdio.h>

int main(void) {
    int value;
    if (scanf("%d", &value) != 1 || value < 0 || value > 255) {
        puts("Invalid input.");
        return 1;
    }
    printf("Binary: ");
    for (int bit = 7; bit >= 0; --bit)
        printf("%d", (value >> bit) & 1);
    putchar('\n');
    return 0;
}
Open in compiler ↗

Code loads into the existing compiler. Enter the sample input there; sign-in and execution rules stay the same.

Compile and run locally
gcc -std=c17 eight-bit-binary.c -o lab
./lab

On Windows, run .\lab.exe after compiling with GCC. The interest program requires the math library where applicable.

FOLLOW THE VALUES

Dry run

Step / stateOperationResult
5 in decimal4 + 100000101
Bit 2(5 >> 2) & 11
Bit 0(5 >> 0) & 11

CHECK THE BEHAVIOR

Sample input & output

Each output below was produced by compiling and running this exact program. Input values are entered in the stated order; the examples do not print input prompts.

Sample 1

INPUT 
5
OUTPUT
Binary: 00000101

Sample 2

INPUT 
0
OUTPUT
Binary: 00000000

Sample 3

INPUT 
255
OUTPUT
Binary: 11111111

Common mistakes

  • Use bitwise & rather than logical && to extract a bit.
  • Validate the range before representing the input as an eight-bit value.

WHY THIS GROWTH RATE?

Time and space complexity

Time O(1) for eight bits; auxiliary space O(1).

The loop always visits exactly eight bit positions, from 7 down to 0. It performs eight shifts, masks and outputs whether the input is 0, 5 or 255.

Because eight is fixed for the specified 0–255 range, time is O(1), and scalar variables use O(1) auxiliary space. A generalized program for a variable b-bit representation would instead take O(b) time.

Big-O describes how work grows as the stated input quantity grows; fixed factors and lower-order terms are omitted. The analysis treats fixed-width arithmetic as constant cost and the published limits as practical safety bounds.