How to Convert an IP Address from Decimal to Binary

An IPv4 address is a 32-bit number. The dotted-decimal form — 192.168.1.10 — exists only because humans find it easier to read. Every router and switch works on the binary underneath, and subnetting only makes sense once you can see it.

Each of the four numbers is one octet — 8 bits, giving a range of 0 to 255.

The Eight Bit Values

Within an octet, each bit position has a fixed value, doubling from right to left:

Those eight numbers sum to 255, which is why that is the maximum value of an octet. Memorising this row is the whole trick — everything else follows from it.

Method 1 — Subtraction (fastest by hand)

Work left to right. At each position ask: does this value fit in what remains? If yes, write 1 and subtract. If no, write 0 and move on.

Converting 192

192 = 11000000

Converting 168

168 − 128 = 40   → 1
 40 − 64        → 0   (64 does not fit)
 40 − 32 = 8    → 1
  8 − 16        → 0
  8 −  8 = 0    → 1
  0 −  4        → 0
  0 −  2        → 0
  0 −  1        → 0

168 = 10101000

The full address

192.168.1.10

192 = 11000000
168 = 10101000
  1 = 00000001
 10 = 00001010

192.168.1.10 = 11000000.10101000.00000001.00001010

Always write all eight bits, padding with leading zeros. 1 is 00000001, not 1 — the padding matters when you line octets up against a mask.

Method 2 — Divide by 2

Divide repeatedly by 2, recording each remainder, then read the remainders bottom to top.

168 ÷ 2 = 84  r 0
 84 ÷ 2 = 42  r 0
 42 ÷ 2 = 21  r 0
 21 ÷ 2 = 10  r 1
 10 ÷ 2 =  5  r 0
  5 ÷ 2 =  2  r 1
  2 ÷ 2 =  1  r 0
  1 ÷ 2 =  0  r 1

Read upward: 10101000

This method is mechanical and hard to get wrong, but slower. The subtraction method is what people use once they know the eight values.

Binary Back to Decimal

Add the position values wherever there is a 1:

11000000 = 128 + 64                    = 192
10101000 = 128 + 32 + 8                = 168
00001010 = 8 + 2                       = 10
11111111 = 128+64+32+16+8+4+2+1        = 255
11111110 = 255 − 1                     = 254

Values Worth Recognising Instantly

Subnet masks only ever use these, because mask bits are contiguous from the left:

Any other value in a subnet mask is invalid — a mask must be a run of 1s followed by a run of 0s, with no gaps.

Why This Matters — Subnetting

A subnet mask separates the network portion of an address from the host portion, and that split can fall anywhere, including partway through an octet. In decimal that is invisible. In binary it is obvious.

Address:  192.168.1.10   = 11000000.10101000.00000001.00001010
Mask /26: 255.255.255.192= 11111111.11111111.11111111.11000000
                            └──────── network ────────┘└ host ┘

To find the network address, AND the two together — the result is 1 only where both are 1:

  00001010   (host octet: 10)
& 11000000   (mask octet: 192)
  --------
  00000000   = 0

Network address: 192.168.1.0/26

To find the broadcast address, set every host bit to 1:

  00111111   = 63

Broadcast: 192.168.1.63
Usable range: 192.168.1.1 – 192.168.1.62

This is the operation every router performs on every packet, and it is why “the same subnet” has a precise meaning rather than an approximate one.

Practising

Convert these, then check them:

• 10.0.0.1
• 172.16.254.1
• 255.255.255.240
• 127.0.0.1

10.0.0.1        = 00001010.00000000.00000000.00000001
172.16.254.1    = 10101100.00010000.11111110.00000001
255.255.255.240 = 11111111.11111111.11111111.11110000
127.0.0.1       = 01111111.00000000.00000000.00000001

Our IP to binary converter shows the working for any address, and the subnet calculator gives network, broadcast and host range for any mask. Once the binary makes sense, subnetting explained and the subnetting cheat sheet are the next step.

Frequently Asked Questions

Why is the maximum octet value 255?

Eight bits with every position set — 128+64+32+16+8+4+2+1 — sums to 255. With 0 included, that is 256 possible values per octet.

Do I need to memorise the bit values?

Knowing 128, 64, 32, 16, 8, 4, 2, 1 makes conversion take seconds instead of minutes, and it is unavoidable for subnetting under exam time pressure. It is the one thing worth memorising.

What is the fastest conversion method?

Subtraction, once you know the eight values. Divide-by-2 is more mechanical and less error-prone if you are just starting.

Why do subnet masks only use certain numbers?

Because mask bits must be contiguous — all the 1s to the left, all the 0s to the right. That produces exactly nine possible octet values: 0, 128, 192, 224, 240, 248, 252, 254 and 255.

How do I find the network address from an IP and mask?

Convert both to binary and AND them — the result is 1 only where both bits are 1. The result is the network address.

Is IPv6 converted the same way?

IPv6 uses hexadecimal rather than decimal, where each hex digit maps to exactly four binary bits. That direct mapping makes it easier to convert, not harder — see IPv4 addressing for the comparison.