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.
Byte: All the discrete information in digital
systems is represented as group of bits. A similar group of 8 bits is called a byte.
Decimal to binary conversion:
Formula to convert a decimal number to binary: Is derived using an example below.
Decimal to binary conversion
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.
a0 = LSB = 1
a1 = left bit to LSB (a0) = 0
a2 = left bit to a1 = 0
A3 = left bit to a2 = 0
A4 = left bit to a3 or most significant bit (MSB) = 1
The equivalent binary number for 17 decimal is = (a4a3a2a1a0) = (10001)
b0 = 0
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)