---
# System prepended metadata

title: 'Beginner : Maths'

---


# Maths

[Class
recording](https://www.scaler.com/meetings/i/beginner-maths-1-6/archive)

[lecture
notes](https://drive.google.com/file/d/1scmwyBmYqBgTv1d8kGS7nISr8ZM2HKUJ/view?usp=share_link)





## **Content**

1.  Number system
2.  Binary number system
3.  Decimal number system
4.  Binary ⟷ decimal representation
5.  Range
6.  Log function





### **Meanwhile when people are joining** (5-7 mins)

-   Instructor's welcome.
-   Breaking ice with students.
-   casual conversation to bond.


---
title: Number System
description:
duration: 200
card_type: cue_card
---


## **Number System**
-   Binary system i.e **0/1**
-   Decimal number system i.e **0,1,2...9**



![download.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/011/original/download_%2812%29.png?1689591622)

-   Correct way of representing a number system is to specify its base.
    e.g (183)<sub>10</sub>, (101)<sub>2</sub> etc.





![download.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/012/original/download_%2813%29.png?1689591640)





-   From left to right, the digits represent increasing powers of 10
    starting from 0.
-   (9456)<sub>10</sub> is 6\* 10<sup>0</sup>+5\* 10<sup>1</sup>+4\*
    10<sup>2</sup>+9\* 10<sup>3</sup>





![download.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/013/original/download_%2814%29.png?1689591659)





-   Number system to base 50, e.g (9456)<sub>50</sub> = 6\*
    50<sup>0</sup>+5\* 50<sup>1</sup>+4\* 50<sup>2</sup>+9\*
    50<sup>3</sup>

-   (-312)<sub>10</sub> is -1\* (3\* 10<sup>2</sup>+2\*
    10<sup>1</sup>+1\* 10<sup>0</sup>)



---
title: Binary number system
description:
duration: 200
card_type: cue_card
---

## **Binary number system**





-   Contains **0s** and **1s** alone.
-   Any number less than 2<sup>*n*</sup> can be represented by n digits





### **Question - What is the value?**


-   (101)<sub>2</sub>
-   (1111)<sub>2</sub>
-   (00000001111)<sub>2</sub>





**Ans**:

-   (101)<sub>2</sub> = 5
-   (1111)<sub>2</sub> = 15
-   (00000001111)<sub>2</sub> = 15





![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/014/original/download_%2815%29.png?1689591705)

**NOTE:** Leading zeros in a number representaton has no significance.





### **Question: Write all binary numbers from 0 to 7.**





![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/015/original/download_%2816%29.png?1689591725)
![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/016/original/download_%2817%29.png?1689591748)

-   Notice how every odd number has the unit digit 1.
    ![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/017/original/download_%2818%29.png?1689591759)

-   first 1 digit of a number in binary representation occurs at the
    biggest power of 2 less than the number
-   for example, for 22 the largest power of 2 less than 22 is 16 or
    2<sup>4</sup> , therefore first 1 occurs at 5th place from right
    (starts from 0).
    ![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/018/original/download_%2819%29.png?1689591809)


---
title: Converting decimal to binary
description:
duration: 300
card_type: cue_card
---

## Converting decimal to binary

-   Progressively divide by the base of the number system you want to
    convert it into and note down the remainder from end to start.



#### Question : Convert decimal number 50 to binary





**Answer:** 110010





![download.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/019/original/download_%2820%29.png?1689591838)





![download.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/020/original/download_%2821%29.png?1689591869)





![download.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/021/original/download_%2822%29.png?1689591886)


---
title: Converting Binary to Decimal conversion
description:
duration: 300
card_type: cue_card
---


## Binary ↔ Decimal conversion





-   Decimal to binary : divide by 2
-   Binary to decimal : multiply powers of 2





![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/023/original/download_%2823%29.png?1689591906)


## **Decimal to binary intuitive method**





-   Progressively take the largest power of **2** less than the number,
    by subtracting the largest power of **2** from the number.





![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/024/original/download_%2824%29.png?1689591924)





### **Difference between number system**

-   Binary number system in just two values 0s and 1s can represent any
    value of number while decimal needs 10 values (0 to 9).


---
title: Explaining Range
description:
duration: 300
card_type: cue_card
---


## Range





-   `The range [1,10]` represents `[1,2,3,4,5,6,7,8,9,10]`
-   Square brackets `[]` means the terminal values are inclusive
-   In square bbrackets `[start, end]`, the number of values is
    **end-start+1**
-   `(1,10)` represents `[2,3,4,5,6,7,8,9]`
-   in round brackets `()`, the terminal values are exclusive.
-   `(start, end)` has **end-start-1** number of values





### **Question: Number of numbers in the range `[100, 302]`**

**Ans**: 302-100+1 = 203





### **Question: Number of numbers in the range `(100, 302)`**

**Ans**: 302-100-1 = 201

-   in `( )` the start is excluded and end is excluded, it is called
    mixed range.





### **Question: Number of numbers in the range `[100, 302)`**

**Ans**: 302-100 = 202





-   in `[ )` the start is excluded and end is excluded, it is called
    mixed range.





-   Python always uses mixed range `[start,end)`





``` python=
range(1,10)
len(range(1,10))
```


```bash=
9
```


---
title: Explaining bin function
description:
duration: 300
card_type: cue_card
---




## `bin()` in python





-   Gives the binary value
-   Binary in python is represented by '0b' prefix




Code:
``` python=
print(bin(56)) #'ob111000
a=0b101
a #5
```

>Output
```bash=
0b111000
5
```







### **Question**: Given a number, find the digit at the unit place

**Ans**: '%'




Code:
``` python=
a = 36279734984
a % 10 #unit place digit
```

>Output
```bash=
4
```







### **Question**: Given a number, find the digit at

1.  List item
2.  List item

the tens place




Code:
``` python=
a = 36279734984
d = a%100
d = d // 10 #tens place digit
d
```

>Output
```bash=
8
```







### Given a number how many times should you divide by 2 to get 1?





**Ans:** `floor(log(n))`





![image.png](https://d2beiqkhq929f0.cloudfront.net/public_assets/assets/000/040/025/original/download_%2825%29.png?1689591953)

The answer would be equal to the closest power of 2 which would be equal
to `floor(log(n))`.



---
title: Explaining Log function
description:
duration: 300
card_type: cue_card
---


### **Log function**

-   a<sup>*x*</sup> = b then, log<sub>*a*</sub>(b) = x





---
title: Quiz-1
description: Quiz-1
duration: 60
card_type: quiz_card
---





# Question


Which of the following is not a valid number system in Python?

# Choices

- [ ] Binary
- [ ] Octal
- [ ] Hexadecimal
- [x] Ternary





---
title: Quiz-2
description: Quiz-2
duration: 60
card_type: quiz_card
---

# Question



What is the output of the following code snippet?
```python=
a = 0b101
b = 0b110
print(bin(a|b))
```
# Choices

- [ ] 0b1010
- [x] 0b111
- [ ] 0b1001
- [ ] 0b10

---
title: Quiz-2 Explanation
description: 
duration: 60
card_type: cue_card
---

### Explanation:
The \| operator performs a bitwise OR operation on the
binary representations of the two numbers. In this case, a OR b results
in the binary number 0b111.





---
title: Quiz-3
description: Quiz-3
duration: 60
card_type: quiz_card
---


# Question


What is the decimal equivalent of the binary number 101011?

# Choices

- [x] 43
- [ ] 45
- [ ] 47
- [ ] 49





---
title: Quiz-4
description: Quiz-4
duration: 60
card_type: quiz_card
---


# Question


What is the output of the following code snippet?
```python=
import math
print(math.log10(100))
```
# Choices

- [x] 2
- [ ] 10
- [ ] 100
- [ ] 0.01

---
title: Quiz-4 Explanation
description: 
duration: 60
card_type: cue_card
---

### Explanation:

Explanation: The `math.log10` function in Python returns the base-10
logarithm of a number. In this case, the input to the function is 100,
which is equal to 10 raised to the power of 2 (i.e., 100 = 10^2).
Therefore, the output of `math.log10(100)` is 2.





---
title: Quiz-5
description: Quiz-5
duration: 60
card_type: quiz_card
---



# Question

What is the output of the following code snippet?
```python=
for i in range(1, 10, 2):
    print(i, end=' ')
```
# Choices

- [x] 1 3 5 7 9
- [ ] 1 4 7
- [ ] 2 4 6 8
- [ ] 2 4 8
