Leading Zeros

Leading zeros are the zeros sitting to the left of the first 1 in a binary pattern. They add nothing to the value, so 00101100 and 101100 mean exactly the same amount. Even so, an 8-bit pattern is normally written out in full with all eight bits, so that every bit keeps its correct place value.

Why the full eight bits are kept

A binary pattern only makes sense when each bit is matched to a place value, and a bit's position is what gives it its worth. Writing to a fixed width of eight holds every bit in its own column and stops bits drifting into the wrong column. A number stored in a computer is held in a fixed number of bits anyway, so those extra zeros at the front are just empty space.

Converting a pattern that starts with zeros

Work through all eight bits in the usual way: line them up under 128, 64, 32, 16, 8, 4, 2 and 1, then add only the place values where a 1 appears. A zero bit contributes 0 × its place value, so each leading zero brings nothing to the total.

Keeping the bits in place

Dropping zeros from the left only works when every remaining bit keeps its place relative to the right-hand end. If a bit slides one column to the left it doubles, so treating 00101100 as 01011000 gives 88 rather than 44. Adding zeros is the same: a zero added on the right doubles the value, while one added at the front changes nothing.