Chapter 5: Numbers & Bits¶

The `int` Type¶

In [1]:

a = 42

In [2]:

id(a)

Out[2]:

94857615440928

In [3]:

type(a)

Out[3]:

int

In [4]:

Out[4]:

In [5]:

1_000_000

Out[5]:

In [6]:

1_2_3_4_5_6_7_8_9

Out[6]:

123456789

In [7]:

  Cell In[7], line 1
    042
    ^
SyntaxError: leading zeros in decimal integer literals are not permitted; use an 0o prefix for octal integers

In [8]:

int(42.11)

Out[8]:

In [9]:

int(42.87)

Out[9]:

In [10]:

int(-42.87)

Out[10]:

-42

In [11]:

int("42")

Out[11]:

Binary Representations¶

Bit $i$	7	6	5	4	3	2	1	0
Digit	$2^7$	$2^6$	$2^5$	$2^4$	$2^3$	$2^2$	$2^1$	$2^0$
$=$	$128$	$64$	$32$	$16$	$8$	$4$	$2$	$1$

In [15]:

bin(3)

Out[15]:

'0b11'

In [16]:

int("0b11", base=2)

Out[16]:

In [17]:

0b11

Out[17]:

In [20]:

bin(0)

Out[20]:

'0b0'

In [23]:

bin(255)

Out[23]:

'0b11111111'

In [24]:

bin(789)

Out[24]:

'0b1100010101'

Arithmetic with Bits¶

In [25]:

1 + 2

Out[25]:

In [26]:

bin(1) + " + " + bin(2) + " = " + bin(3)

Out[26]:

'0b1 + 0b10 = 0b11'

In [27]:

1 + 3

Out[27]:

In [28]:

bin(1) + " + " + bin(3) + " = " + bin(4)

Out[28]:

'0b1 + 0b11 = 0b100'

In [29]:

4 * 3

Out[29]:

In [30]:

bin(4) + " * " + bin(3) + " = " + bin(12)

Out[30]:

'0b100 * 0b11 = 0b1100'

In [31]:

bin(4) + " * " + bin(1) + " = " + bin(4)  # multiply with first digit

Out[31]:

'0b100 * 0b1 = 0b100'

In [32]:

bin(4) + " * " + bin(2) + " = " + bin(8)  # multiply with second digit

Out[32]:

'0b100 * 0b10 = 0b1000'

Hexadecimal Representations¶

Decimal	Hexadecimal	Binary	$~~~~~~$	Decimal	Hexadecimal	Binary	$~~~~~~$	Decimal	Hexadecimal	Binary	$~~~~~~$	...
0	0	0000	$~~~~~~$	16	10	10000	$~~~~~~$	32	20	100000	$~~~~~~$	...
1	1	0001	$~~~~~~$	17	11	10001	$~~~~~~$	33	21	100001	$~~~~~~$	...
2	2	0010	$~~~~~~$	18	12	10010	$~~~~~~$	34	22	100010	$~~~~~~$	...
3	3	0011	$~~~~~~$	19	13	10011	$~~~~~~$	35	23	100011	$~~~~~~$	...
4	4	0100	$~~~~~~$	20	14	10100	$~~~~~~$	36	24	100100	$~~~~~~$	...
5	5	0101	$~~~~~~$	21	15	10101	$~~~~~~$	37	25	100101	$~~~~~~$	...
6	6	0110	$~~~~~~$	22	16	10110	$~~~~~~$	38	26	100110	$~~~~~~$	...
7	7	0111	$~~~~~~$	23	17	10111	$~~~~~~$	39	27	100111	$~~~~~~$	...
8	8	1000	$~~~~~~$	24	18	11000	$~~~~~~$	40	28	101000	$~~~~~~$	...
9	9	1001	$~~~~~~$	25	19	11001	$~~~~~~$	41	29	101001	$~~~~~~$	...
10	a	1010	$~~~~~~$	26	1a	11010	$~~~~~~$	42	2a	101010	$~~~~~~$	...
11	b	1011	$~~~~~~$	27	1b	11011	$~~~~~~$	43	2b	101011	$~~~~~~$	...
12	c	1100	$~~~~~~$	28	1c	11100	$~~~~~~$	44	2c	101100	$~~~~~~$	...
13	d	1101	$~~~~~~$	29	1d	11101	$~~~~~~$	45	2d	101101	$~~~~~~$	...
14	e	1110	$~~~~~~$	30	1e	11110	$~~~~~~$	46	2e	101110	$~~~~~~$	...
15	f	1111	$~~~~~~$	31	1f	11111	$~~~~~~$	47	2f	101111	$~~~~~~$	...

In [33]:

hex(0)

Out[33]:

'0x0'

In [34]:

hex(1)

Out[34]:

'0x1'

In [36]:

hex(10)

Out[36]:

'0xa'

In [37]:

hex(15)

Out[37]:

'0xf'

In [38]:

bin(123)

Out[38]:

'0b1111011'

In [39]:

hex(123)

Out[39]:

'0x7b'

In [40]:

int("0x7b", base=16)

Out[40]:

In [41]:

0x7b

Out[41]:

In [42]:

hex(0)

Out[42]:

'0x0'

In [43]:

hex(255)

Out[43]:

'0xff'

In [44]:

hex(789)

Out[44]:

'0x315'

Bitwise Operators¶

In [49]:

11 & 13

Out[49]:

In [53]:

9 | 13

Out[53]:

In [61]:

~7

Out[61]:

-8