20 min read

Number Systems in Real Life

Hex colour codes, memory addresses, network addresses and Linux file permissions — where binary, octal and hex appear.

Hexadecimal Colour Codes

Screens make every colour by mixing red, green and blue light (RGB). Each of the three uses one byte : a value from 0 to 255. One byte is exactly two hex digits, so a colour is written as six hex digits after a # : #RRGGBB — two digits for red, two for green, two for blue.

Worked example

Reading Hillside Print House's brand colour #813588

Channel Hex Decimal Red 81 8 \times 16 + 1 = 129 Green 35 3 \times 16 + 5 = 53 Blue 88 8 \times 16 + 8 = 136 Red and blue are fairly high, green is low: the result is a purple . Ishara types #813588 in Photoshop and on the website so the brand colour is exactly the same everywhere.

Colour mixer (RGB)

Red129 → 81Green53 → 35Blue136 → 88

Hex: #813588

rgb(129, 53, 136)

≈ CMYK 5% 61% 0% 47%

The CMYK figures use a simple formula. Real print conversion (for example in Photoshop) uses colour profiles, so the numbers will differ a little.

Try it:

Move the sliders. Each channel's decimal value (0-255) and its two hex digits update together.

Every byte in memory has a numbered address . Addresses are large binary numbers, so they are shown in hex. The printer's error message 0x7F3A means address 7F3A₁₆ = 32,570₁₀. The 0x in front is the usual way programs mark a hex number. Hex is shorter than binary and converts to it instantly: 7F3A₁₆ = 0111 1111 0011 1010₂. An engineer can see the exact bits at a glance.

A MAC address identifies a network card. It is six bytes written in hex, for example 3C:52:82:1A:9F:07 . An IPv4 address such as 192.168.1.20 is four bytes written in decimal. Each part is 0-255 because each part is one byte. In binary, 192 is 11000000. The newer IPv6 addresses are written in hex because they are 128 bits long, for example 2001:db8::1.

Linux and macOS give every file three sets of permissions — for the owner, the group and others . Each set has three yes/no switches: read (r), write (w) and execute (x) . Three bits \to exactly one octal digit .

Worked example

What does chmod 750 mean?

Who Owner Group Others Octal 750 Bits 111101000 Permissions rwx r-x --- The owner can do everything, the group can read and run the file, and everyone else has no access. Nuwan uses this on the file server so only staff can open customer designs.

Setting permissions on a Linux serverCommand line

1chmod 750 customer-designs2ls -l3drwxr-x--- 2 nuwan staff 4096 Mar 12 09:15 customer-designs

Practice

In the colour code #1E90FF, what is the green value in decimal?

Hexadecimal Colour Codes

Screens make every colour by mixing red, green and blue light (RGB). Each of the three uses one byte : a value from 0 to 255. One byte is exactly two hex digits, so a colour is written as six hex digits after a # : #RRGGBB — two digits for red, two for green, two for blue.

Worked example

Reading Hillside Print House's brand colour #813588

Channel Hex Decimal Red 81 8 \times 16 + 1 = 129 Green 35 3 \times 16 + 5 = 53 Blue 88 8 \times 16 + 8 = 136 Red and blue are fairly high, green is low: the result is a purple . Ishara types #813588 in Photoshop and on the website so the brand colour is exactly the same everywhere.

Colour mixer (RGB)

Red129 → 81Green53 → 35Blue136 → 88

Hex: #813588

rgb(129, 53, 136)

≈ CMYK 5% 61% 0% 47%

The CMYK figures use a simple formula. Real print conversion (for example in Photoshop) uses colour profiles, so the numbers will differ a little.

Try it:

Move the sliders. Each channel's decimal value (0-255) and its two hex digits update together.

Memory Addresses

Every byte in memory has a numbered address . Addresses are large binary numbers, so they are shown in hex. The printer's error message 0x7F3A means address 7F3A₁₆ = 32,570₁₀. The 0x in front is the usual way programs mark a hex number. Hex is shorter than binary and converts to it instantly: 7F3A₁₆ = 0111 1111 0011 1010₂. An engineer can see the exact bits at a glance.

Network Addresses

A MAC address identifies a network card. It is six bytes written in hex, for example 3C:52:82:1A:9F:07 . An IPv4 address such as 192.168.1.20 is four bytes written in decimal. Each part is 0-255 because each part is one byte. In binary, 192 is 11000000. The newer IPv6 addresses are written in hex because they are 128 bits long, for example 2001:db8::1.

Octal File Permissions in Linux

Linux and macOS give every file three sets of permissions — for the owner, the group and others . Each set has three yes/no switches: read (r), write (w) and execute (x) . Three bits \to exactly one octal digit .

Worked example

What does chmod 750 mean?

Who Owner Group Others Octal 750 Bits 111101000 Permissions rwx r-x --- The owner can do everything, the group can read and run the file, and everyone else has no access. Nuwan uses this on the file server so only staff can open customer designs.

Setting permissions on a Linux serverCommand line

1chmod 750 customer-designs2ls -l3drwxr-x--- 2 nuwan staff 4096 Mar 12 09:15 customer-designs

Practice

In the colour code #1E90FF, what is the green value in decimal?