Here we have two different types of arithmetic system, on one hand 'modulus' (or clock) arithmetic and on the other hand, place value systems (which use different number bases). Unlike modulus arithmetic, where many numbers are represented by the same symbol, in base arithmetic each distinct number has its own distinct representation different from that of any other number.

The table compares counting in the two systems, using arithmetic modulo 7 and numbers in base 7 as an example. The units digit of a number in base 7 is the same as the equivalent number in arithmetic modulo 7.