How to convert hexadecimal to binary (example: 9C)
The simplest way is to go through decimal (or through binary): convert hexadecimal 9C to decimal (156), then convert decimal to binary (10011100). Shortcut: each octal digit equals 3 binary digits and each hex digit equals 4 binary digits, so you can group bits directly.
Place value chart
Every digit of 9C (base 16) is worth its value multiplied by a power of 16. Adding the last column gives the decimal value 156.
| Digit | Place value | Contribution |
|---|---|---|
9 | 161 = 16 | 144 |
C | 160 = 1 | 12 |
Remember: in base 2 the allowed digits are 01; in base 16 they are 0123456789ABCDEF.
Hexadecimal to Binary table
| Hexadecimal | Binary |
|---|---|
0 | 0 |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
7 | 111 |
8 | 1000 |
A | 1010 |
F | 1111 |
10 | 10000 |
19 | 11001 |
20 | 100000 |
32 | 110010 |
40 | 1000000 |
64 | 1100100 |
7F | 1111111 |
80 | 10000000 |
FF | 11111111 |
100 | 100000000 |
200 | 1000000000 |
3E8 | 1111101000 |
400 | 10000000000 |
7EA | 11111101010 |
Where number systems are used
- Binary — how CPUs, memory and network packets store every value.
- Octal — Unix/Linux file permissions such as chmod 755.
- Hexadecimal — colour codes (#FF5733), MAC addresses, memory dumps and Unicode code points.
- Decimal — everyday arithmetic, prices and measurements.
About these number systems
Hexadecimal
Hexadecimal (base 16) uses 0–9 and A–F, common in programming, colour codes and memory addresses.
Binary
Binary (base 2) uses only 0 and 1. Every digital device stores data in binary.
Frequently asked questions
What is 9C (hexadecimal) in binary?
9C in base 16 equals 10011100 in base 2.
Can it convert very large numbers?
Yes. The converter uses arbitrary-precision integers (BigInt), so large numbers convert exactly.
Is this useful for HSC ICT?
Yes. Number systems are part of the HSC ICT syllabus in Bangladesh, and the step-by-step method matches textbook solutions.