Binary / Hex / 2s Complement

Lecture 6 - January 17th, 2017

Why Binary?

  • Binary is how computers talk
    • to themselves AND
    • to each other

Decimal Numbers

A binary abacus -> Example

Question: 101 is 5 in binary

1 0 1
2^2 2^1 2^0 
1x2^2 + 0x2^1 + 1x2^0

1x4 + 0x2 + 1x1 = 5

Binary Number Example

NOTE: Test Material

Question: What is 11111 in decimal number?

Answer: 31

Question: What is the highest number you can encode with n bits?

Answer: 2^n -1

Encode Numbers

Note: If the decimal number is a perfect power of two, it will be easy to find, but if it's not you have two methods.

Method 1

5 = 4 + 1

So 2^2 and 2^0

So 00101 = 5

Method 2

Step1   input: number_in cur_number = number_in binary_string = “”
Step2   while cur_number >= 2
Step3       my_encoding = input%2
Step4       add my_encoding to leW side of binary string 
Step5       cur_number = round_down(cur_number/2)
Step6   add cur_number to leW side of binary string

Question: What is 11 in binary?

num_in = 11

binary_string=""
11%2 = 1

binary_string="1"

11/2 = 5.5 -> 5
5%2 = 1

binary_string="11"

5/2 = 2.5 -> 2
2%2 = 0

binary_string="011"

2/2 = 1

binary_string="1011"

Question: What is 8 in binary? 

num_in = 8 

binary_string=""
8%2 = 0

binary_string="0"

8/2 = 4
4%2 = 0

binary_string="00"

4/2 = 2
2%2 = 0

binary_string="000"

2/1 = 1

binary_string="1000"

NOTE: Practice on your own.

Lecture 7 - January 18th, 2017

Helper: Question 2 - Assignment 1

  • Input for this program is a list of numbers.
  • Pseudo code for addition. 
a(m-1), a(m-2), a(1), a(0)
4 3 7
a(m-1) a(m-2) a(0)

Answer: m=3

3 2 9
b(2) b(1) b(0) 
437+329=766

Draw a flow chart

  • Use draw.io
  • Export as an image
  • Hand in PDF

Binary Numbers

10110 = 22
01001 = 9

Tip: If it ends with a 1 it is odd. If it ends in a 0 it is even.

8 -> 01000 5 -> 00101

Algorithm Decimal Number - Binary.

Ex. Binary Conversion

binary_string=""

23%2 = 1

binary_string=1

23/2 = 11.5 -> 11
11%2 = 1

binary_string=11

11/2 = 5.5 > 5
5%2=1

binary_string=111

5/2=2.5 -> 2
2%2=0

binary_string=0111

2/2 = 1

binary_string=10111

Note: If a question ask for 5 bit number, you must include 5 places.

Adding Binary Numbers

Ex. 00111+00001=01000

1 1 1
0 0 1 1 1
+
0 0 0 0 1
=
0 1 0 0 0

Bonus: 00111+00111=01110

1 1 1
0 0 1 1 1
+
0 0 1 1 1
=
0 1 1 1 0

Encoding Negative Numbers

  1. Encode the positive number
  2. Flip all the bits (1->0 and 0->1)
  3. Add 1 to the new bit string

Question: Convert -9 into binary

01001
10110
10111

Question: Convert 12 into binary

01100
10011
10100

Two's complement number

NOTE: Unsigned Binary Number or a Two's Complement Number.

Ignore overflow that carries in Two's compliment

Convert Two's complement into decimal

  1. If negative:
    • Flip a bit and add one
    • Put the negative back at the end
  2. If positive:
    • Normal Conversion

Lecture 8 - January 20th, 2017

Notes Missing

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