Alternating Binary Number Triangle Pattern in PHP

Beginner

⏱️ 8 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Modulo Operator

Alternating binary number triangle output (1, 01, 101, 0101, 10101) in PHP programming

Overview

What You’ll Learn

The alternating binary number triangle combines nested loops with the modulo operator to print 0 and 1 in an alternating sequence. This tutorial covers the shape rule, loop structure, a live preview, algorithm steps, worked PHP examples, edge cases, and complexity.

Shape Rule

j % 2 alternates 0 and 1

Row 1 prints 1, row 2 prints 01, row 3 prints 101, and so on as width grows.

Outer Loop

Rows

for ($i = 1; $i <= $rows; $i++) makes each new row one digit longer than the previous.

Inner Loop

i..1 descending

for ($j = $i; $j >= 1; $j--) prints $j % 2 while counting down, creating the alternating binary row.

echo vs PHP_EOL

Same line / next line

Binary digits use echo $j % 2; end each row with echo PHP_EOL.

Live Preview

1–20 rows

Pick a row count and draw the alternating binary triangle instantly in the browser.

O(n²)

Complexity

Total digit prints still = n(n+1)/2; extra memory stays O(1).

Introduction

An alternating binary number triangle grows each row by one digit while alternating between 0 and 1 using the modulo operator. With rows = 5, the output is 1, 01, 101, 0101, 10101.

In PHP you solve it with an ascending outer loop and a descending inner loop: for ($j = $i; $j >= 1; $j--) prints $j % 2, then echo PHP_EOL; ends each row.

Why it matters?

It is a fun way to practice parity and nested loops before more complex logic-heavy patterns.

Key Highlights

Modulo Alternation

j % 2 yields 0 for even j, 1 for odd j.

Descending Inner Loop

j = i down to 1 sets digit order on each row.

Print Then Break

echo $j % 2 in the inner loop; echo PHP_EOL after.

Series Foundation

Follow Program 14; continue to Program 16 (ascending inner loop).

In short: for each row i from 1 to rows, print j % 2 for j from i down to 1, then call echo PHP_EOL.

Foundation

📝 Problem & Approach

Given a positive integer rows, print an alternating binary number triangle: row i has i digits from j % 2 as j counts down from i to 1.

PHP

// rows = 5 (conceptual shape)
// 1
// 01
// 101
// 0101
// 10101

Inputs & Outputs

Item	Type	Description
`rows`	int	Number of triangle lines to print (typically ≥ 1).
Printed output	text	Each row has `i` alternating binary digits from `j % 2`.

Minimal workflow

Pseudocode

for i from 1 to rows:
    for j from i down to 1:
        print j % 2 (no newline)
    print newline

Approach comparison

Approach	Idea	Best for
Descending inner + `j % 2`	1, 01, 101, …	Learning and interviews
Flip with `1 - (j % 2)`	Start rows with 0 instead of 1	Parity inversion variant

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Walk each row	`for ($i = 1; $i <= $rows; $i++)`
Print binary digit	`for ($j = $i; $j >= 1; $j--) echo $j % 2;`
End the row	`echo PHP_EOL;`
Flip parity	`echo 1 - ($j % 2);`
Program 16 variant	`for ($j = 1; $j <= $i; $j++) echo $j % 2` (ascending inner)
Row + column parity	`echo ($i + $j) % 2;`

Compare

📋 j % 2 vs Flip vs Ascending Inner

Same binary triangle family — different ways to emit 0 and 1.

j % 2

parity

Even j → 0, odd j → 1

1 - (j % 2)

flipped

Inverts every digit — row 1 starts with 0

j down to 1

desc inner

This page — produces 1, 01, 101, …

Learning tip

% 2 first

Master j % 2 before row+column parity

Context

When This Pattern Shows Up

Reach for this pattern when teaching the modulo operator inside nested loops.

First lab exercise
Most PHP pattern series start here before pyramids and diamonds.
Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with fgets(STDIN) for a flexible row count.
Gateway to variants
Compare Program 14 (odd-length rows) and Program 16 (ascending inner loop) next.
Not a UI layout tool
This is a console teaching pattern — not how you build modern app screens.

Key benefit: one small program that locks in nested loops, output sequencing, and O(n²) thinking.

Interactive

🔮 Live Preview

Choose a row count between 1 and 20 and draw the alternating binary triangle in the browser.

Hands-On

Examples Gallery

Three complete PHP programs — fixed rows, a flip variant, and a user-input version. Click View Output to reveal sample console results.

📚 Getting Started

Print five rows of the alternating binary triangle with j % 2.

Example 1 — Fixed `rows = 5`

Hard-coded height — ideal for first demos and screenshots.

PHP

<?php
$rows = 5;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $i; $j >= 1; $j--) {
        echo $j % 2;
    }
    echo PHP_EOL;
}

How It Works

When i = 1, the inner loop prints 1 % 2 = 1. When i = 3, it prints 3%2=1, 2%2=0, 1%2=1 as 101, and so on as row width grows. echo PHP_EOL after the inner loop starts the next row.

📈 Flip Variant

Invert parity so the first row starts with 0 instead of 1.

Example 2 — Flip with `1 - (j % 2)`

Start each row with 0 instead of 1 by inverting the parity output.

PHP

<?php
$rows = 5;

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $i; $j >= 1; $j--) {
        echo 1 - ($j % 2);
    }
    echo PHP_EOL;
}

How It Works

1 - (j % 2) flips every digit: where j % 2 was 1 it prints 0, and vice versa. Row 1 becomes 0 instead of 1.

⚡ User Input

Read the row count at runtime and scale the binary triangle.

Example 3 — User Input Version

Read $rows with (int) trim(fgets(STDIN)) and apply the same $j % 2 logic.

PHP

<?php
echo "Enter the number of rows: ";
$rows = (int) trim(fgets(STDIN));

for ($i = 1; $i <= $rows; $i++) {
    for ($j = $i; $j >= 1; $j--) {
        echo $j % 2;
    }
    echo PHP_EOL;
}

How It Works

Same nested-loop core as Example 1; only the source of rows changes. Non-numeric input leaves rows unset if you skip is_numeric() checks — always check it in safer labs.

🧠 How the Algorithm Prints Rows

Set up

Set $rows = 5; and use fgets(STDIN) when reading input. Set rows (fixed or from input).

Setup

Outer loop (row length)

for ($i = 1; $i <= $rows; $i++) makes each row one digit longer than the previous.

Row

Inner loop (modulo)

for ($j = $i; $j >= 1; $j--) prints $j % 2 with echo to alternate 0 and 1.

Binary

New line

echo PHP_EOL ends the row so the next outer iteration starts fresh.

Break

Binary triangle complete

Total digit prints: 1+2+…+n = n(n+1)/2 — O(n²) time, O(1) extra memory.

Trace

🔎 Worked Walkthrough — `rows = 4`

Trace each outer-loop value of i and note the j % 2 values printed on each row.

`i`	Inner `j` order	`j % 2` values	Printed row
`1`	`1`	`1`	`1`
`2`	`2, 1`	`0, 1`	`01`
`3`	`3, 2, 1`	`1, 0, 1`	`101`
`4`	`4, 3, 2, 1`	`0, 1, 0, 1`	`0101`

Total digit prints: 1 + 2 + 3 + 4 = 10 = 4×5/2.

Use Cases

Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.

1. Teaching Nested Loops

Clearest visual proof that outer and inner bounds interact.

Example: change j <= i and watch the shape change.

2. Pattern Series Base

Foundation for inverted, pyramid, diamond, and hollow variants.

Example: use (i + j) % 2 for row+column parity grids.

3. Console Formatting Drills

Practice echo vs PHP_EOL without complex math.

Example: put echo PHP_EOL inside the inner loop by mistake.

4. Character Substitution

Swap digits for letters, stars, or spaced output once the loop works.

Example: print j + " " for spaced digits on each row.

5. Complexity Intuition

Triangular totals make O(n²) concrete for beginners.

Example: count printed digits for n = 10 still → 55.

6. Input Validation Labs

Pair the pattern with fgets(STDIN) and is_numeric() checks and positive-row checks.

Example: reject rows <= 0 and re-prompt.

Pro Tip: when an interviewer asks for patterns, explain the outer/inner roles first — then write the loops. The story matters as much as the code.

Advantages

Why this pattern earns a permanent spot in beginner C courses.

1. Instant Visual Feedback
Wrong bounds show up immediately as a broken staircase.
2. Minimal Concepts
Only loops and console output — no arrays or math libraries.
3. Easy to Extend
Invert, center, hollow, or change the fill character with small edits.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.

Pro Tip: learn j % 2 first; compare with 1 - (j % 2) to flip every digit on each row.

Usage Tips

Small habits that keep number-pattern code clean.

1. Name Bounds Clearly
Use rows (or n) and keep i/j for row/column — or rename to row/col.
2. Validate CLI input
Call is_numeric(trim($line)) so bad input does not leave rows uninitialized.
3. Keep echo PHP_EOL Outside
Only call echo PHP_EOL after the inner loop finishes the row.
4. Trace j % 2 on Paper
Write the j values and their modulo before coding — catches direction mistakes early.
5. Dry-Run One Small n
Trace rows = 5 on paper before coding larger demos.

Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put echo PHP_EOL inside the inner loop.

Common Pitfalls

Mistakes that commonly break alternating binary number patterns.

1. Newline Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use echo $j % 2 for binary digits; echo PHP_EOL only after the inner loop.
2. Wrong Inner Direction
Counting j up instead of down changes row ordering (see Program 16).
→ For this shape, keep for ($j = $i; $j >= 1; $j--).
3. Forgetting the Row Break
Omitting echo PHP_EOL glues every digit onto one endless line.
→ Always end the row after the inner loop.
4. Unchecked CLI input
Letters or empty input leave rows uninitialized.
→ Prefer is_numeric() and re-prompt on failure.
5. Off-by-One on 0-Based Loops
Switching to i = 0 without adjusting the inner bound prints an empty first row or wrong counts.
→ If 0-based, print i with wrong inner bound (e.g. j <= i + 1).

Edge Cases

Check these inputs before calling the solution done.

rows = 1

Single digit

Output is just 1 on one line.

rows = 0

Empty pattern

Outer loop never runs — print nothing or show a message.

Negative

`rows < 0`

Treat as invalid; re-prompt instead of silent empty output.

Large n

Many rows

Output grows as n²/2 characters — fine for labs, noisy for huge n.

Bad input

Non-numeric CLI input

Unchecked fgets(STDIN) leaves rows unset — call is_numeric(trim($line)) first.

Fill char

Forgot modulo

echo $j prints 1,2,3… — use echo $j % 2 for binary output.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Odd-length descending triangle

Outer loop i -= 2 for odd widths only
Continue with Program 14

2. Ascending inner binary triangle

Inner loop j = 1 to i instead of down
Continue with Program 16

3. Flip parity

Use 1 - (j % 2) so row 1 starts with 0
Compare output with Example 2

4. Spaced binary output

Use echo $j % 2 between digits
Harder follow-up after this page

Important

Notes

Triangular sum. Digit prints for rows 1+2+3+…+n still grow as O(n²) for n rows.
echo $j % 2 stays on the line; echo PHP_EOL advances — mix them carefully.
Validate rows > 0 for interactive programs; rows = 1 should print a single 1.
This page is left-aligned. Centered pyramids need leading spaces — covered later in the series.

Quick Takeaway: outer loop grows row length, inner loop prints j % 2 descending, then break the line.

Analysis

⏱️ Time and Space Complexity

Program	Time	Extra space
Nested loops (Examples 1–2)	`O(rows²)`	`O(1)`
User input (Example 3)	`O(rows²)`	`O(1)`

Wrap Up

🎉 Conclusion

The alternating binary number triangle is a compact lesson in modulo inside nested loops. Master the j % 2 version, then try the flip variant with 1 - (j % 2).

Practice the three examples above, then continue to Program 16 for the ascending-inner-loop binary triangle.

Use $j % 2 for alternating 0/1 — keep echo for digits and echo PHP_EOL; for the break, and validate row counts when reading input.

View Examples Gallery Continue to Program 16

Pro Tips

💡 Best Practices

✅ Do

Explain j % 2 before coding descending inner loop
Use echo $j % 2 for digits and echo PHP_EOL after each row
Validate rows ≥ 1 for interactive programs
Call is_numeric(trim($line)) before using rows
State O(n²) time when asked about complexity

❌ Don’t

Call echo PHP_EOL inside the inner digit loop
Print j directly instead of j % 2
Count j up when you meant this page’s descending inner loop
Skip the newline after each row
Ignore bad console input in user-facing demos
Skip the rows = 1 edge case

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this binary pattern

Print the pattern the beginner-friendly way.

Core concepts

△ 01

Rule

j % 2 alternates 0 and 1

Definition

↻ 02

Outer loop

Grows row length each line

Code

% 03

Modulo

j % 2 picks digit

Logic

↵ 04

Newline

Ends each row

I/O

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

Why does j % 2 print only 0 or 1?

Modulo 2 returns the remainder after dividing by 2. Any integer is either even (remainder 0) or odd (remainder 1).

Why does the second row print 01?

On row 2, the inner loop prints j = 2 then j = 1. That becomes 2 % 2 = 0 then 1 % 2 = 1, so the row is 01.

What is the difference between echo and PHP_EOL?

echo $j % 2 stays on the same line. echo PHP_EOL ends the current line. Binary digits use echo; the row break uses echo PHP_EOL after the inner loop.

Why does row 3 print 101?

Row 3 prints j = 3, 2, 1 and j % 2 becomes 1, 0, 1 — concatenated as 101.

How is this different from Program 16?

Program 15 counts the inner loop down (j = i to 1) producing 1, 01, 101, 0101, 10101. Program 16 counts up (j = 1 to i) producing 1, 10, 101, 1010, 10101.

Can I start each row with 0 instead of 1?

Yes. Print 1 - (j % 2) instead of j % 2 to flip every digit — first row becomes 0 instead of 1.

What is the time complexity?

O(n²) where n is the number of rows. Total digit prints equal n+(n-1)+…+1 = n(n+1)/2.

How should I read the row count safely?

Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int so bad input does not produce unexpected results.

What happens if rows is 0 or negative?

The outer loop never runs, so nothing is printed. Validate and prompt again if you want a clear user message.

Did you Know? 🔊

Each row prints alternating 0 and 1 using $j % 2. The inner loop counts down from $i to 1, so row length grows each line — still O(n²) total prints.

Continue to Program 16

Move on to the column-wise alternating binary pattern in the PHP number-pattern series.

Program 16 tutorial →

About the author

Mari Selvan M P 🔗

Developer, cloud engineer, and technical writer

Experience 12 years building web and cloud systems
Focus Full Stack Development, AWS, and Developer Education

I write practical tutorials so students and working developers can learn by doing—from databases and APIs to deployment on AWS.

AWS Certified Developer – Associate (Credly)

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PHP Number Pattern 14 — Odd-Length Descending Pyramid PHP Number Pattern 16 — Column-Wise Alternating Binary

Alternating Binary Number Triangle Pattern in PHP

What You’ll Learn

Shape Rule

Outer Loop

Inner Loop

echo vs PHP_EOL

Live Preview

O(n²)

Introduction

Why it matters?

Modulo Alternation

Descending Inner Loop

Print Then Break

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 j % 2 vs Flip vs Ascending Inner

When This Pattern Shows Up

First lab exercise

Nested-loop warm-up

Console I/O practice

Gateway to variants

Not a UI layout tool

🔮 Live Preview

Examples Gallery

📚 Getting Started

Example 1 — Fixed rows = 5

How It Works

📈 Flip Variant

Example 2 — Flip with 1 - (j % 2)

How It Works

⚡ User Input

Example 3 — User Input Version

How It Works

🧠 How the Algorithm Prints Rows

Set up

Outer loop (row length)

Inner loop (modulo)

New line

Binary triangle complete

🔎 Worked Walkthrough — rows = 4

Use Cases

1. Teaching Nested Loops

2. Pattern Series Base

3. Console Formatting Drills

4. Character Substitution

5. Complexity Intuition

6. Input Validation Labs

Advantages

1. Instant Visual Feedback

2. Minimal Concepts

3. Easy to Extend

4. O(1) Extra Memory

Usage Tips

1. Name Bounds Clearly

2. Validate CLI input

3. Keep echo PHP_EOL Outside

4. Trace j % 2 on Paper

5. Dry-Run One Small n

Common Pitfalls

1. Newline Inside the Inner Loop

2. Wrong Inner Direction

3. Forgetting the Row Break

4. Unchecked CLI input

5. Off-by-One on 0-Based Loops

Edge Cases

Single digit

Empty pattern

rows < 0

Many rows

Non-numeric CLI input

Forgot modulo

🎯 Practice Problems

1. Odd-length descending triangle

2. Ascending inner binary triangle

3. Flip parity

4. Spaced binary output

Example 1 — Fixed `rows = 5`

Example 2 — Flip with `1 - (j % 2)`

🔎 Worked Walkthrough — `rows = 4`

`rows < 0`