Binary Number System
This number system is back-bone of the digital electronics.
This number system has the minimum possible and useful base (radix) i.e. 2. This is because base-0 system is not possible and base-1 number system is not useful.
Every number in this system is denoted by using two symbols: 0 and 1.
The left-most bit is called as Most Significant Bit (MSB) and right-most bit is called as Least Significant Bit (LSB).
This number system has the minimum possible and useful base (radix) i.e. 2. This is because base-0 system is not possible and base-1 number system is not useful.
Every number in this system is denoted by using two symbols: 0 and 1.
The left-most bit is called as Most Significant Bit (MSB) and right-most bit is called as Least Significant Bit (LSB).
Symbols in any binary number are called BInary digiTS, or bits in general.
A group of 4-bits is called a nibble.
A group of 8-bits is called a byte.
And, a group of 16-bits is generally called a word. (In fact, a word is said to group of any number of bits, that signify something; e.g. if a digital message has 12-bits to convey info, word length is 12-bit , as in 12-bit ADC. But, generic notation is like 16-bit: word, 32-bit: double-word etc.)
A group of 4-bits is called a nibble.
A group of 8-bits is called a byte.
And, a group of 16-bits is generally called a word. (In fact, a word is said to group of any number of bits, that signify something; e.g. if a digital message has 12-bits to convey info, word length is 12-bit , as in 12-bit ADC. But, generic notation is like 16-bit: word, 32-bit: double-word etc.)
Complementary numbers
Like those for decimal numbers, the complement numbers do exist for binary numbers also. For binary number, 2's complement and 1's complement numbers exists.
(1's complement of N) = 2^n - N
(2's complement of N) = 2^n - N + 1
Instead of performing subtraction, 1's complement can also be found just by complementing the number bit-by-bit.
e.g. N = (1010)b = (10)d
so, n = 4
(1's complement of 1010) = 2^4 - 1010
= 1111 - 1010
= 0101
and we can see that 1010 and 0101 are two numbers complement to each other bit-by-bit.
( 2's complement of 1010) = (1's complement of 1010) + 1
= 0101 + 1 = 0111
(1's complement of N) = 2^n - N
(2's complement of N) = 2^n - N + 1
Instead of performing subtraction, 1's complement can also be found just by complementing the number bit-by-bit.
e.g. N = (1010)b = (10)d
so, n = 4
(1's complement of 1010) = 2^4 - 1010
= 1111 - 1010
= 0101
and we can see that 1010 and 0101 are two numbers complement to each other bit-by-bit.
( 2's complement of 1010) = (1's complement of 1010) + 1
= 0101 + 1 = 0111
Complements of binary numbers play an important role in arithmetic digital circuits like subtractor.
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1's complement and 2's complement of any binary number exists . . . |
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0 1 0 1 0 1 0 1 0 1