This document contains an exercise on digital electronics concepts including: 1. The differences between analog and digital measurements and pros and cons of analog vs digital electronics. 2. Tables defining binary, octal, decimal, and hexadecimal number systems. 3. Practice problems converting between number systems and performing basic binary math operations like addition, subtraction, multiplication, and division. 4. An independent practice section with additional problems converting between number systems and performing binary math.

1. 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

2. 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

3. 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 0and
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

4. 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

5. 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

6. 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