Discrete Mathematics

Number system Handout

Prepared by:

Joseph Malkevitch
Department of Mathematics and Computer Studies
York College (CUNY)
Jamaica, New York 11451

1. The decimal system is based on the idea that:

347 represents 3(10)2 + 4(10)1 + 7(10)0

since (10)2 is defined to mean 10 (10) = 100

we have 347 represents 300 + 40 + 7 which is the number three hundred forty seven.

The reason we use powers of 10 is that in the decimal system we have 10 symbols including the symbol for zero.

Assuming the the digits 0, 1, 2, ...., 9 have their usual meaning and using the ideas above:

a. What number (write it down in words) is represented by:

223 in a system with 5 symbols (0, 1, 2, 3, 4).

b. What number (write it down is words) is represented by:

1011101 in a system with 2 symbols (0, 1).

c. What number (write it down in words) is represented by:

12002 in a system with 3 symbols (0, 1, 2).

2. What number is represented (write it down in words and Hindu-arabic symbols) by the following expressions in Roman:

a. XLV

b. MCXXIV

c. CCCXLIV