Why 16 is a convenient partner for 2
16 is a power of 2 (2⁴ = 16), which means every hex digit (0 to f, values 0-15) can be written as exactly 4 binary digits — 0000 through 1111 — with no leftover or overlap. That clean fit is what makes converting between hex and binary a matter of direct substitution rather than arithmetic.
A worked example, decimal 42
Decimal 42 converts to binary as 101010 (6 digits) and to hex as "2a" (2 digits). Padding the binary out to a multiple of 4 digits gives 00101010, which splits cleanly into two 4-digit groups: 0010 and 1010. The first group, 0010, is 2 in decimal — matching the hex digit "2". The second group, 1010, is 10 in decimal — matching the hex digit "a". Grouping the binary digits four at a time reads off the hex digits directly, with no division or place-value multiplication required.
Converting hex to binary the same way, in reverse
The same grouping works backwards: each hex digit expands to its own fixed 4-digit binary block. "2" becomes 0010 and "a" becomes 1010, so "2a" becomes 00101010 — which, once the leading zeros are dropped, is 101010, the same binary value computed directly from decimal 42 in the companion article on binary and decimal conversion.
When this shortcut matters
Converting hex to decimal and decimal to binary separately — as in the two companion articles — always gets the right answer, but it's two rounds of arithmetic. The 4-bit grouping shortcut skips decimal entirely: it's why hexadecimal shows up throughout computing (color codes, memory addresses, byte values) as a compact way to write binary data that a person can actually read at a glance, rather than counting through a long string of 0s and 1s.