# Binary Notation: Place-Value for the Computer Era

(1)

Here’s how you count from 1 to 12 in binary.

Write the decimal equivalent next to each number.

0 0

1 1

10 2

11 3

100 4

101 5

110 6 you add up the 1’s

111 7 giving each a value according to its place

1000 8

1001 9

1010 10 (this is one 8 plus one 2)

1011 11

1100 12

Try to understand the pattern.

How would you write 14 in binary?

What does 10000 as a binary number represent?

(2) How is 45 written in binary?

(3) What decimal number is written as 10101101 in binary?

(4) Try the usual addition method in a binary version:

1010 + 101 = ?

1011 + 1 = ?

1111 + 1111 = ?

Check your answers, by converting all the numbers (the numbers being added, and your answers) into decimal.

(5)

Try the usual subtraction method in its binary version:

1101 – 101 = ?

110 – 1 = ?

1000 – 1 = ?

Check your answers, by converting all the numbers (the numbers being added, and your answers) into decimal.

Now try multiplication:

1101

1010

—-

and check your result, converting both factors and the product into decimal.

Study these examples first, as a hint:

1011 1011

11 101

—- —-

1011 1011

1011 1011

—— ——

100001 110111

Divide 11011 (binary) by 101 (binary) using the ordinary method.

Check your result, converting all numbers into decimal

Here’s an example, as a hint:

110 (quotient)

.——

100| 11001

100

—

100

100

—

1 (remainder)

In the decimal system, the fraction 1/3 is written as 0.333…

What happens with 1/3 in binary?