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Step3:- 4/2 = 2 + 0

    a2 = left bit to a1 = 0

Step4:- 2/2 = 1 + 0

    A3 = left bit to a2 = 0

Step5

   A4 = left bit to a3 or most significant bit (MSB) = 1

The equivalent binary number for 17 decimal is = (a4a3a2a1a0) = (10001)

Step6:- 0.25*2 = 0.50 + 0

     b0 = 0

Step7:- 0.50*2 = 0.00 + 1

     b1 = 1

The equivalent binary number for 0.25 decimal is = (0.b0b1) = (0.01)

Answer The equivalent binary number for 17.25 decimal = (a4a3a2a1a0.b0b1) = (10001.01)

Binary to Decimal conversions:

Formula to convert a binary number to decimal: Is derived using an example below.

Example: Convert 101010.1 to decimal

The equivalent decimal value

= 1*(2^5) + 0*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 0*(2^0) + 1*(2^-(1))

= 32 + 0 + 8 + 0 + 2 + 0 + 0.5

= 42.5

Answer. The decimal equivalent of (101010.1) is 42.5

Hexadecimal numbers

Group of 4 bits can also be represented as hexadecimal numbers. Refer Table below.

Decimal to binary conversion conversions:

Formula to convert a decimal number to binary: Is derived using an example below.

Example: To represent 17.25 in digital system we will need to use 5 bits.

Step1: - 17/2 = 8 + ½

     a0 = LSB = 1

Step2: - 8/2 = 4 + 0

    a1 = left bit to LSB (a0) = 0

Binary Numbers Discussion

Bit: The smallest unit of a digital system is called a ‘bit’. A bit can take one of the two  logical values of  1 or 0. A set of 4 bits can represent (=2^4) 16 decimal values. And a set of 5 bits can represent (=2^5) 32 decimal values... and so on.

 

 

 

 

 

 

 

Unsigned
Binary
Hexadecimal
0
0000
0
1
0001
1
2
0010
2
3
0011
3
4
0100
4
5
0101
5
6
0110
6
7
0111
7
8
1000
8
9
1001
9
10
1010
A
11
1011
B
12
1100
C
13
1101
D
14
1110
E
15
1111
F
Interview Questions. Main, FPGA, Digital Fundamentals
Byte: All the discrete information in digital systems is represented as group of bits. A similar group of 8 bits is called a byte.