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Complement number Discussion

Binary Numbers.

1s_complement.

2s_complement.

Binary Subtraction.

Examples.

Sign_magnitude.

Gray coding.

BCD coding.

Digital gates.

NAND NOR & XNOR.

Theorems.

Boolean Functions.

BFunc Examples.

Minterm Maxterm.

Sum of Minterms.

Prdt of Maxterms.

2 var K-map.

3 var K-map.

4 var K-map.

5 var K-map.

Prime Implicant.

PI example.

1’ s Complement Discussion

Binary numbers can also be represented by ‘radix’ and ‘radix -1’ forms.

1’s complement of a binary number N is obtained by the formula  : -(2^n – 1) – N

Where n is the no of bits in number N

Example

Convert binary number 111001101 to 1’s complement

Method:

N = 111001101

n = 9

2^n = 256 = 100000000

2^n -1 = 255 = 11111111

1’s complement of N = (100000000 – 1) -111001101

    011111111

 – 111001101

 = 000110010

Answer:

1’s complement of N is 000110010

Trick:

Invert all the bits of the binary number

N = 111001101

1’s complement of N is 000110010