Question

Express the binary strings in the left column of the following table in hexadecimal notation in the right column of the table.

Binary string	Binary string expressed in hexadecimal notation
1111000011110000
1010111010101110
1111000111011111
11110000110110001101
10001100111011111000

Add the bit strings in the first two columns of the following table and report the answer in the last column in binary notation.

Bit string 1	Bit string 2	Result of the addition in binary notation
111101	111110
100010	110011
111011	101111
110001	100001
1111101	1001111

Answer 1

Binary Number: Combination or pair of two digits 0 and 1 is called binary number. it is used in digital communication and networking.

Binary representation of Decimal number:

Binary number is multiplication of power of 2 i.e (2ⁿ).

Ex--> so on upto n .........2⁶ ,2⁵ ,2⁴ ,2³ ,2² ,2¹ , 2⁰ (we write it from right to left to make a binary number)

Lets consider a decimal number 16 and conver it into binary notation with the help of multiplication of power of 2.

step1: 9 ---> 8, 4, 2,1 (here we 8 and 1 to get 9 [8+1=9])

2³ ,2² ,2¹ , 2⁰(break the number in to multiple of 2).

step2: 9---->  8 , 4,2,1 (Put 1 at 1 and 1 at 8 hence aading of 8 and 1 we will get 9.)

1, , , 1

Step3: 9----> 1,0,0,1 (here we dont need 4 and 2 to get 9 so after that put every weher 0)

Note: - Ignore commas(,) in step3

Decimal	Binary
0	000
1	001
2	010
3	011
4	100
5	101
....so on	...so on

Hexadecimal Number: Hexadecimal number is a combination of 6(Hexa) alphabet(A,B,C,D,E,F) and 9 decimal numbers. hence it has only 16 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , A, B, C, D, E, F. where A, B, C, D, E and F are single bit representations of decimal value 10, 11, 12, 13, 14 and 15 respectively.

Binary representation of Hexadecimal number:

Decimal number	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A(10)	1010
B(11)	1011
C(12)	1100
D(13)	1101
E(14)	1110
F(15)	1111

Solution of the above question:

Express the binary strings in the left column of the following table in hexadecimal notation in the right column of the table.

1. 1111000011110000

Step1: ( ( 1111 ) ( 0000 ) ( 1111 ) ( 0000 ) )₁₆Make the 4 bit pair of given number

Step2: Now consider the above decimal to Hexadecimal table and match the notation/number from that table and write it as it is here with base value 16.

so according to table 1111 is the representation of F and 0000 is for 0(zero). so we will replace these vale with 4 bit pair of the given number.

step3: hence final hexadecimal number of givine binary number is (F0F0)₁₆

Note: You can do it with above binary number example without taking help of hexadecimal table also in case you dont remember the table.

Further solution of given binary notations are similar like this:

Binary String	4-bit pair	Expressedin Hexadecimal notaion
1010111010101110	(1010 1110 1010 1110)16	(AEAE)16
1111000111011111	(1111 0001 1101 1111)16	(F1DF)16
11110000110110001101	(1111 0000 1101 1000 1101)16	(F0D8D)16
10001100111011111000	(1000 1100 1110 1111 1000)16	(8CEF8)16

2. Add the bit strings in the first two columns of the following table and report the answer in the last column in binary notation.

Rules of Binary Addition:

A + B	Sum	Carry
0 + 0	0	0
0 + 1	1	0
1 + 0	1	0
1 + 1	0	1

Here at the last row 1 + 1 = 10 but we write 0 only and it carry 1.

example-->

1 1 1 <---------- Carry

1 1 1 1 0 1

+ 1 1 1 1 1 0

1 1 1 1 0 1 1

further similarly for other given binary notataion:

String1	Addition	string2	Result
100010	+	110011	01010101
111011	+	101111	01101010
110001	+	100001	01010010
1111101	+	1001111	011001100

Note : if above solution helped you understand the concept of binary and hexadecimal notation then like and commen on this post.