11: Digital principles

Example number 11.1, Page number 408

In [136]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='1001101';    #binary number

#Calculation
b=int(a,2);    #number in decimal form

#Result
print "number in decimal form is",b

number in decimal form is 77

Example number 11.2, Page number 408

In [137]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='1001.101';    #binary number

#Calculation
def parse_bin(s):
    t = s.split('.')
    return int(t[0], 2) + int(t[1], 2) / 2.**len(t[1])

n=parse_bin(a);    #number in decimal form

#Result
print "number in decimal form is",n

number in decimal form is 9.625

Example number 11.3, Page number 409

In [138]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='246';     #octal number

#Calculation
n=int(a,8);    #number in decimal form

#Result
print "number in decimal form is",n

number in decimal form is 166

Example number 11.4, Page number 409

In [139]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='136.24';     #octal number

#Calculation
def parse_bin(s):
    t = s.split('.')
    return int(t[0], 8) + int(t[1], 8) / 8.**len(t[1])

n=parse_bin(a);    #number in decimal form

#Result
print "number in decimal form is",n

number in decimal form is 94.3125

Example number 11.5, Page number 410

In [140]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='4FE';     #hexadecimal number

#Calculation
n=int(a,16);    #number in decimal form

#Result
print "number in decimal form is",n

number in decimal form is 1278

Example number 11.6, Page number 411

In [141]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='10';    #binary number

#Calculation
b=int(a,2);    #number in decimal form

#Result
print "number in decimal form is",b

number in decimal form is 2

Example number 11.7, Page number 411

In [142]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='11111';    #binary number

#Calculation
b=int(a,2);    #number in decimal form

#Result
print "number in decimal form is",b

number in decimal form is 31

Example number 11.8, Page number 412

In [143]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=41;     #decimal number

#Calculation
n=bin(a);    #binary equivalent

#Result
print "binary equivalent is",n

binary equivalent is 0b101001

Example number 11.9, Page number 412

In [144]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=0.65625;     #decimal number

#Calculation
x1=a*2;
n1=int(x1);   #carry
x2=(x1-n1)*2;
n2=int(x2);   #carry
x3=x2*2;
n3=int(x3);   #carry
x4=(x3-n3)*2;
n4=int(x4);   #carry
x5=x4*2;
n5=int(x5);   #carry

#Result
print "since the given decimal number is fractional the binary equivalent will be 0.",n1,n2,n3,n4,n5

since the given decimal number is fractional the binary equivalent will be 0. 1 0 1 0 1

Example number 11.10, Page number 413

In [145]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='110111.101';    #binary number

#Calculation
def parse_bin(s):
    t = s.split('.')
    return int(t[0], 2) + int(t[1], 2) / 2.**len(t[1])

n=parse_bin(a);    #number in decimal form

#Result
print "number in decimal form is",n

number in decimal form is 55.625

Example number 11.11, Page number 413

In [146]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='1001';    #binary number
b='1111';    #binary number

#Calculation
sum=int(a,2)+int(b,2);    #sum of two binary numbers
sum=bin(sum);

#Result
print "sum of two binary numbers is",sum

sum of two binary numbers is 0b11000

Example number 11.12, Page number 414

In [147]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='011';    #binary number
b='101';    #binary number

#Calculation
diff=int(b,2)-int(a,2);    #difference of two binary numbers
diff=bin(diff);

#Result
print "difference of two binary numbers is",diff

difference of two binary numbers is 0b10

Example number 11.13, Page number 415

In [148]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='1011';    #binary number
b='0110';    #binary number

#Calculation
diff=int(a,2)-int(b,2);    #difference of two binary numbers
diff=bin(diff);

#Result
print "difference of two binary numbers is",diff

difference of two binary numbers is 0b101

Example number 11.14, Page number 415

In [149]:
#importing modules
import math
from __future__ import division

#Variable declaration
n='010'    #binary number

#Calculation
def complement(n):
    size = len(format(n, 'b'))
    comp = n ^ ((1 << size) - 1)
    return '0b1{0:0{1}b}'.format(comp, size)

a=complement((0b010))

#Result
print "1's complement of the number is",a

1's complement of the number is 0b101

Example number 11.15, Page number 415

In [150]:
#importing modules
import math
from __future__ import division

#Variable declaration
n='1110'    #binary number

#Calculation
def complement(n):
    size = len(format(n, 'b'))
    comp = n ^ ((1 << size) - 1)
    return '0b{0:0{1}b}'.format(comp, size)

a=complement((0b1110))

#Result
print "1's complement of the number is",a

1's complement of the number is 0b0001

Example number 11.16, Page number 416

In [152]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='1011';    #binary number
b='1101';    #binary number

#Calculation
diff=int(b,2)-int(a,2);    #difference of two binary numbers
diff=bin(diff);

#Result
print "difference of two binary numbers is",diff

difference of two binary numbers is 0b10

Example number 11.17, Page number 416

In [153]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='1100';    #binary number
b='1000';    #binary number

#Calculation
diff=int(b,2)-int(a,2);    #difference of two binary numbers
diff=bin(diff);

#Result
print "difference of two binary numbers is",diff

difference of two binary numbers is -0b100

Example number 11.18, Page number 416

In [154]:
#importing modules
import math
from __future__ import division

#Variable declaration
n='0101'     #binary number
b='1'

#Calculation
def complement(n):
    size = len(format(n, 'b'))
    comp = n ^ ((1 << size) - 1)
    return '0b1{0:0{1}b}'.format(comp, size)

a=complement((0b0101))
ans=int(a,2)+int(b,2);     #2's complement of number

#Result
print "2's complement of number is",bin(ans)

2's complement of number is 0b1011

Example number 11.19, Page number 417

In [155]:
#importing modules
import math
from __future__ import division

#Variable declaration
n='101100'     #binary number
b='1'

#Calculation
def complement(n):
    size = len(format(n, 'b'))
    comp = n ^ ((1 << size) - 1)
    return '0b{0:0{1}b}'.format(comp, size)

a=complement((0b101100))
ans=int(a,2)+int(b,2);     #2's complement of number

#Result
print "2's complement of number is",bin(ans)

2's complement of number is 0b10100

Example number 11.20, Page number 417

In [156]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=bin(6);
b=bin(2);

#Calculation
c= int(a,2)-int(b,2);    #difference

#Result
print "difference is",bin(c)

difference is 0b100

Example number 11.21, Page number 418

In [157]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=bin(3);
b=bin(5);

#Calculation
c=int(a,2)-int(b,2);    #difference

#Result
print "difference is",bin(c)

difference is -0b10

Example number 11.22, Page number 420

In [158]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='01101110'    #binary number

#Calculation
ans=hex(int(a,2));    #equivalent hexadecimal number

#Result
print "equivalent hexadecimal number is",ans

equivalent hexadecimal number is 0x6e

Example number 11.23, Page number 420

In [159]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='10110101111011'    #binary number

#Calculation
ans=hex(int(a,2));    #equivalent hexadecimal number

#Result
print "equivalent hexadecimal number is",ans

equivalent hexadecimal number is 0x2d7b

Example number 11.24, Page number 421

In [160]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='1100111111011'    #binary number

#Calculation
ans=hex(int(a,2));    #equivalent hexadecimal number

#Result
print "equivalent hexadecimal number is",ans

equivalent hexadecimal number is 0x19fb

Example number 11.25, Page number 421

In [161]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='11001110001'    #integral part of binary number
b='000101111001';    #fractional part of binary number

#Calculation
c=hex(int(a,2));    #converting into hexadecimal number
d=hex(int(b,2));    #converting into hexadecimal number

#Result
print "equivalent hexadecimal number is",c,".",d

equivalent hexadecimal number is 0x671 . 0x179

Example number 11.26, Page number 421

In [162]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='6B9';    #umber in hexadecimal

#Calculation
def float_to_binary(num):
    exponent=0
    shifted_num=num
    while shifted_num != int(shifted_num):        
        shifted_num*=2
        exponent+=1
    if exponent==0:
        return '{0:0b}'.format(int(shifted_num))
    binary='{0:0{1}b}'.format(int(shifted_num),exponent+1)
    integer_part=binary[:-exponent]
    fractional_part=binary[-exponent:].rstrip('0')
    return '{0}.{1}'.format(integer_part,fractional_part)

def floathex_to_binary(floathex):
    num = float.fromhex(floathex)
    return float_to_binary(num)

ans=(floathex_to_binary('6B9'));     #equivalent binary number    

#Result
print "equivalent binary number is",ans   

equivalent binary number is 11010111001

Example number 11.27, Page number 421

In [163]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='6D.3A';    #number in hexadecimal

#Calculation
def float_to_binary(num):
    exponent=0
    shifted_num=num
    while shifted_num != int(shifted_num):        
        shifted_num*=2
        exponent+=1
    if exponent==0:
        return '{0:0b}'.format(int(shifted_num))
    binary='{0:0{1}b}'.format(int(shifted_num),exponent+1)
    integer_part=binary[:-exponent]
    fractional_part=binary[-exponent:].rstrip('0')
    return '{0}.{1}'.format(integer_part,fractional_part)

def floathex_to_binary(floathex):
    num = float.fromhex(floathex)
    return float_to_binary(num)

ans=(floathex_to_binary('6D.3A'));     #equivalent binary number    

#Result
print "equivalent binary number is",ans   

equivalent binary number is 1101101.0011101

Example number 11.28, Page number 422

In [164]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=5000;    #decimal number

#Calculation
ans=hex(a);    #equivalent hexadecimal number

#Result
print "equivalent hexadecimal number is",ans

equivalent hexadecimal number is 0x1388

Example number 11.29, Page number 422

In [165]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=14619;    #decimal number

#Calculation
ans=hex(a);    #equivalent hexadecimal number

#Result
print "equivalent hexadecimal number is",ans

equivalent hexadecimal number is 0x391b

Example number 11.30, Page number 422

In [166]:
#importing modules
import math
from __future__ import division

#Variable declaration
a=15101;    #decimal number

#Calculation
ans=hex(a);    #equivalent hexadecimal number

#Result
print "equivalent hexadecimal number is",ans

equivalent hexadecimal number is 0x3afd

Example number 11.31, Page number 423

In [167]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='4B8';    #hexadecimal number

#Calculation
ans=int(a,16);    #equivalent decimal number

#Result
print "equivalent decimal number is",ans

equivalent decimal number is 1208

Example number 11.32, Page number 423

In [168]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='3A4B';    #hexadecimal number

#Calculation
ans=int(a,16);    #equivalent decimal number

#Result
print "equivalent decimal number is",ans
print "answer given in the book is wrong"

equivalent decimal number is 14923
answer given in the book is wrong

Example number 11.33, Page number 424

In [169]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='2B6D';    #number in hexadecimal

#Calculation
ans=int(a,16);    #equivalent decimal number

#Result
print "equivalent decimal number is",ans   

equivalent decimal number is 11117

Example number 11.34, Page number 424

In [170]:
#importing modules
import math
from __future__ import division

#Variable declaration
a='FC2';    #number in hexadecimal
b='DAB';    #number in hexadecimal

#Calculation
ans=int(a,16)-int(b,16);    #difference of two numbers
ans=hex(ans);

#Result
print "difference of two numbers is",ans

difference of two numbers is 0x217