Binary and hexadecimal for networking: conversions by hand, mask values, powers of two and hex in MAC/IPv6

Computers store everything as bits: 0 or 1. An IPv4 address like 192.168.1.10 is really 32 bits, and a subnet mask like 255.255.255.0 is 32 bits too. Subnetting, which is the skill every network engineer needs (and every networking exam tests), is just counting and switching bits. Once binary feels natural, subnetting becomes easy.

Hexadecimal (hex) is a shorter way to write binary. You'll see it in MAC addresses (3C:52:82:1A:0F:9B), IPv6 addresses (2001:db8::1), colour codes in web design (#FF6600) and error codes.

Why binary?

Electronics are reliable at telling two states apart: voltage on/off, light on/off, magnetised one way or the other. So computers count in base 2 (two digits: 0 and 1) instead of base 10.

Networking says octet for 8 bits because historically "byte" wasn't always 8 bits.

Place values in one octet

In decimal, each position is worth 10× the one to its right (1, 10, 100...). In binary, each position is worth 2×:

All eight bits on = 128+64+32+16+8+4+2+1 = 255, which is why each octet of an IP address goes from 0 to 255.

Binary to decimal

Add the place values wherever there's a 1.

So 11000000.10101000.00000001.00001010 = 192.168.1.10.

Decimal to binary (subtraction method)

Go through the place values from 128 down. If the value fits into what's left, write 1 and subtract; otherwise write 0.

Convert 200:

200 = 11001000.

Check yourself with Python:

def to_binary(n):
    bits = ""
    for place in [128, 64, 32, 16, 8, 4, 2, 1]:
        if place <= n:
            bits += "1"
            n -= place
        else:
            bits += "0"
    return bits

for n in [200, 172, 10, 255, 99]:
    print(n, "=", to_binary(n), "| check:", format(n, "08b"))

ip = "192.168.1.10"
print(".".join(to_binary(int(o)) for o in ip.split(".")))

Numbers to memorise: mask values

Subnet masks are made of 1s followed by 0s. These are the only values a mask octet can take:

Trick: each value is the previous one plus half the remaining gap: 128, +64 = 192, +32 = 224, +16 = 240, +8 = 248, +4 = 252, +2 = 254, +1 = 255.

Powers of two

Why they matter:

• Host bits h give 2ʰ addresses, of which 2ʰ − 2 are usable hosts (one for the network, one for broadcast). 8 host bits → 256 addresses → 254 hosts.
• Borrowed bits b give 2ᵇ subnets. Borrow 3 bits → 8 subnets.

Hexadecimal

Hex is base 16: digits 0–9, then A=10, B=11, C=12, D=13, E=14, F=15. One hex digit is exactly 4 bits, so one byte is two hex digits.

Converting

• Hex → binary: replace each digit with its 4 bits. C0 → 1100 0000.
• Binary → hex: split into groups of 4 from the right. 1010 1000 → A8.
• Hex → decimal: first digit × 16 + second digit. A8 = 10×16 + 8 = 168. FF = 15×16 + 15 = 255.
• Decimal → hex: divide by 16; the quotient is the first digit, the remainder the second. 192 ÷ 16 = 12 remainder 0 → C0.

for n in [192, 168, 10, 255, 172]:
    print(n, "-> hex", format(n, "02X"), "-> binary", format(n, "08b"))
print("Hex A8 is", int("A8", 16), "in decimal")

Where hex appears in networking

MAC addresses: 48 bits written as 6 pairs of hex digits: 3C:52:82:1A:0F:9B (Windows shows 3C-52-82-1A-0F-9B; Cisco shows 3c52.821a.0f9b). The first 3 bytes (the OUI) identify the manufacturer.

IPv6 addresses: 128 bits written as 8 groups of 4 hex digits: 2001:0db8:0000:0000:0000:0000:0000:0001, shortened to 2001:db8::1 (the IPv6 lesson explains the rules).

Try the converter

Type in any box; the others update. The row shows which bits are on.

This part of the lesson has an interactive tool. Open the live lesson to use it.

Practice

Convert without a calculator, then check with the converter:

1. 11110000 → decimal
2. 172 → binary
3. 100 → binary
4. 0x3F → decimal
5. 224 → hex
6. 10111111 → decimal

Summary

• Computers use binary because two states are reliable; an octet is 8 bits with place values 128, 64, 32, 16, 8, 4, 2, 1.
• Binary → decimal: add the places with 1s; decimal → binary: subtract from 128 down.
• Memorise mask values 128, 192, 224, 240, 248, 252, 254, 255 and powers of two.
• h host bits give 2ʰ − 2 usable hosts; b borrowed bits give 2ᵇ subnets.
• Hex digits are 4 bits each (A=10 ... F=15); hex appears in MAC and IPv6 addresses.

Learn more: Khan Academy: binary numbers · Cisco binary game