Such a number is the sum of terms of the form {a digit times a different power of 10} - we say that 10 is the

All computers today use the *binary system*. This has obvious
hardware advantages, since the only digits in this system are
0 and 1. In the binary system the number is represented as the sum of
terms of the form
{a digit times a different power of 2}. For example,

Arithmetic operations in the binary system are performed similarly as in the decimal system; since there are only 2 digits, 1+1=10.

**Decimal to binary conversion.**
For the integer part, we divide by 2 repeatedly (using integer
division); the remainders are the successive digits of the number
in base 2, from least to most significant.

For the fractional part, multiply the number by 2;
take away the integer part, and multiply the fractional part
of the result by 2, and so on;
the sequence of integer parts are the digits of the base 2 number,
from most to least significant.

**Octal representation.**
A binary number can be easily represented in base 8.
Partition the number into groups of 3 binary digits
(), from decimal point
to the right and to the left (add zeros if needed).
Then, replace each group by its
octal equivalent.

**Hexadecimal representation.**
To represent a binary number in base 16
proceed as above, but now
partition the number into groups of 4 binary digits ().
The base 16 digits are 0,...,9,A=10,...,F=15.

- Convert the following binary numbers to decimal, octal and hexa: 1001101101.0011, 11011.111001;
- Convert the following hexa numbers to both decimal and binary: 1AD.CF, D4E5.35A;
- Convert the following decimal numbers to both binary and hexa: 6752.8756, 4687.4231.