ET 255 Digital I Pre Class Exercise 2 (Print) Name ______________________

1. What is the difference between analog and digital measurements? 2. List some pros and cons of Analog and Digital Electronics (create a chart if useful)

3. Please fill out the following chart

Base # of Digits Digits Usage

Binary 2 Two 0, 1 Digital Computing

(On or Off)

Octal 8 Eight 0, 1, 2, 3, 4, 5, 6, 7 Unix Permissions

& teaching Hexadecimal

Decimal 10 Ten 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Number System used by modern civilizations

Hexadecimal 16

Sixteen 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Compact notion of binary data

Convert the following binary numbers into decimal:

4) 111 5) 1011 6) 11101001

Please stop here until further instruction ---------------------------------------------------------------------------------------

ET 255 Digital I Binary Mathematics (Print) Name ______________________ Notes: Mathematical Operations in Binary

Before you begin, please understand the following concepts Recall the binary conversions for the following decimals:

Binary Power Equivalent: 2 1 x 2 1 x 2 1 x 2 1 Binary Number: 0 0 0 1 1 0 1 1 Decimal Calculation: 0+0 0+1 2+0 2+1 Decimal Number: 0 1 2 3

This gives us the following table:

Decimal Binary

0 00

1 01

2 10

3 11

Decimal Operations the following additions yield

1 0 0 1 1 + 0 + 1 + 1 + 1

0 1 2 3

Binary Operations In binary, we get the same answers that we did in decimal. Just

now, the numbers are represented in binary… aka 1 + 1 + 1 is still 3 it's just that 3 is the number "11" in binary

1 0 0 1 1 + 0 + 1 + 1 + 1

0 1 1 0 1 1

the following subtractions yield

0 1 1 2 - 0 - 0 - 1 - 1

0 1 0 1

In binary subtraction we have the following

0 1 1 1 0 - 0 - 0 - 1 - 1

0 1 0 1

Mathematical Operations in Binary Addition and Subtraction Addition Addition example 1

1 0 2 + 1 + 1

1

1 0 2 + 1 + 1

1 1 3

Addition example 2

1 1 0 6 + 0 1 1 + 3

1

1 1 0 6 + 0 1 1 + 3

0 1

1 Carried 1 1 1 0 6 + 0 1 1 + 3

0 1

1 Carried 1 1 1 0 6 + 0 1 1 + 3

1 0 0 1 9

Try some out!! Double Check by converting to Decimal

Subtraction Subtraction example 1

1 1 3 - 1 - 1

1 0

1 1 3 - 1 - 1

1 0 2

Subtraction example 2

1 0 1 5 - 0 1 1 - 3

0

1 0 1 5 - 0 1 1 - 3

0

0 10 1 5 - 0 1 1 - 3

1 0

0 10 1 5 - 0 1 1 - 3

0 1 0 2

Ex. 1 1 1 + 1 1

Ex. 2 1 0 0 + 1 0

Ex. 3 1 1 1 + 1 1

Ex. 4 1 1 0 1 + 1 1 1

Ex. 5

1 1 - 1 0

Ex. 6

1 1 0 1 - 0 1 1

Ex. 7

1 1 1 1 - 1 0 1

Ex. 8

1 1 1 0 - 1 1 0 1

Multiple Number Additions

Ex. 9

0 1 0

0 0 1

+ 1 1 0

Ex. 10

0 0 1

1 0 1

+ 1 1 1

Ex. 11

1 0 0 0

0 1 0 1

0 1 1 1

+ 0 0 1 1

Ex. 12 1 0 0 0

0 0 1 1

0 1 1 1

1 1 0 1

+ 0 1 1 1

Borrow 1 Carry 1

Mathematical Operations in Binary Multiplication and Division Multiplication

We multiply binary numbers just like we do in Decimal (doing partial products then shifting)

1 0 0 4 x 1 1 1 x 7

First we multiply the first number by everything first…

1 0 0 4 x 1 1 1 x 7

0

1 0 0 4 x 1 1 1 x 7

0 0

1 0 0 4 x 1 1 1 x 7

1 0 0

Next we multiply the second number

1 0 0 4 x 1 1 1 x 7

1 0 0 0

1 0 0 4 x 1 1 1 x 7

1 0 0 0 0

1 0 0 4 x 1 1 1 x 7

1 0 0 1 0 0

Last we multiply the third number

1 0 0 4 x 1 1 1 x 7

1 0 0 1 0 0 0

1 0 0 4 x 1 1 1 x 7

1 0 0 0 0 0 0

1 0 0 4 x 1 1 1 x 7

1 0 0 1 0 0 1 0 0

Now we just add the three together

1 0 0 4 x 1 1 1 x 7

1 0 0 2 8 1 0 0 + 1 0 0

1 1 1 0 0 and

Division Binary division is the same as decimal division

Ex 1.

1 1 1 1 0 0 3 1 2

First we divide the '11' into the first term

0 0

1 1 1 1 0 0 3 1 2

First we divide the '11' into the 11

0 1 0

1 1 1 1 0 0 3 1 2 - 1 1

0 0 0

Since '11' goes into 00, zero times we get

0 1 0 0

1 1 1 1 0 0 3 1 2 - 1 1

0 0

Since '11' goes into 000, zero times we get

0 1 0 0 0 4

1 1 1 1 0 0 3 1 2 - 1 1

0 0 0

The final answer would be 0100 = 4 Ex 2.

1 0 1 0 1 1 0 2 2 2

0 1

1 0 1 0 1 1 0 2 2 2

0 1 1

1 0 1 0 1 1 0 2 2 2 - 1 0

0 1

0 1 0 1

1 0 1 0 1 1 0 2 2 2 - 1 0

0 1

0 1 0 1 1 1

1 0 1 0 1 1 0 2 2 2 - 1 0

0 1 1 - 1 0

0 1

0 1 0 1 1 1 1

1 0 1 0 1 1 0 2 2 2 - 1 0

0 1 1 - 1 0

1 0 - 1 0

0

The final answer would be 01011 = 11 And

Now let's try some out!!!

Ex. 9 1 1 x 1 1

Ex. 10 1 0 0 x 1 0

Ex. 11 1 1 1 x 1 1

Ex. 12 1 1 0 1 x 1 1 1

Ex. 13

1 0 1 1 0

Ex. 14

1 0 1 1 1 0 0

Ex. 15

1 0 1 1 1 0 1 0

Ex. 16

1 0 1 1 1 1 1 0

Independent Practice

3. 1 0 1 + 1 1

4. 1 0 0 0 - 1 0 0

5. 1 1 1 x 1 1

6.

1 0 1 1 1 0

7. 1 0 0 0 x 1 0 1

8. 1 1 1 1 + 1 0

9.

1 0 0 1 0 1 0 0

10.

1 1 1 0 0 1 0

11. 1 1 0 1 - 1 0 1 1

12. 1 0 0 1 x 1 1 0

13.

1 0 1 1 0 1 0 0

14. 1 0 1 1 0 0 1 + 1 1 1

ET 255 Digital 1 Hw 2 (Print) Name ______________________

1. The binary equivalent of 12410 is

2. What is the decimal equivalent of 100101112? 3. Add the binary numbers 1011012 and 101012. Starting from the right, which places generate a carry?

Loc 6 Loc 5 Loc 4 Loc 3 Loc 2 Loc 1

1 0 1 0 1 + 1 0 1 1 0 1

4. What is the result of multiplying the binary numbers 10012 and 1102? 5. What is the hexadecimal equivalent of 7310 ? 6. What is the octal equivalent of 100101002?

7. 1 1 1 0 - 1 1

8. 1 0 1 1 x 1 1

9.

1 1 1 1 1 1 0

10. 1 0 1 1 1 0 0 1 + 1 0 1

11. What is the hexadecimal result of adding B316 and 2A16? 12. How many bits are required to display 3210

in binary?

13. Convert 4110

to binary.

14. Add the following binary numbers: 10011012 + 00110102 15. Add the following: E316

+ 1916

16. Add the following binary numbers: 11012 + 11102 17. How can you tell if a binary number is odd or even?

18. 1 1 0 1 + 1 1 1 1

19. 1 0 1 0 - 1 0 1

20. 1 1 1 0 0 x 1 0 1

21.

1 0 1 0 1 0