Binary Coded Decimal is a 4-bit code used to represent the numeric data alone.

(i) ASCII - American Standard Code for Information Interchange.
(ii) ISCII - Indian Standard Code for Information Interchange

(i) EBCDIC - Extended Binary Coded Decimal Interchange Code
(ii) BCD - Binary Coded Decimal

The coding scheme is used to represent a character in the bits

(i) One's complement of 1010₂ is 0101₂ (replace 1by 0 and 0 by 1)
(ii) One's complement of 100101₂ is 011010₂

The term complement refers to a part which together with another makes up a whole. The one's complement performs the logical negation on each individual bit.

(COFFEE)₁₆
\(\overset { C }{ \underset { 1100 }{ \downarrow } } \)\(\overset { O }{ \underset { 0000 }{ \downarrow } } \)\(\overset { F }{ \underset { 1111 }{ \downarrow } } \)\(\overset { F }{ \underset { 1111 }{ \downarrow } } \)\(\overset { E }{ \underset { 1110 }{ \downarrow } } \)\(\overset { E }{ \underset { 1110 }{ \downarrow } } \)
(COFFEE)₁₆  = (110000001111111111101110)₂

(FACE)₁₆
\(\overset { F }{ \underset { 1110 }{ \downarrow } } \) \(\overset { A}{ \underset { 1111 }{ \downarrow } } \)\(\overset { C }{ \underset { 1010 }{ \downarrow } } \)\(\overset { E }{ \underset { 1110 }{ \downarrow } } \)
(FACE)₁₀  (1111101011001110)₂

(i) The absolute value is the magnitude of a digit in a number.
(ii) For example, the digit 5 in 7458 has an absolute value of 5 according to its value in the number line.
(iii) The place value of a digit in a number refers to the position of the digit in that number such as tens, hundreds, and thousands.
(iv) The total value of a number is the sum of the absolute value x place value of each digit that the number consists of.
(v) The base value of a number is also known as the radix, which depends on the type of the number of systems that are being used.

(300)₁₀ \(\rightarrow \)(100101100)₂ \(\rightarrow \) (454)₈ \(\rightarrow \) (12C)₁₆

101010₂
= 0010  0010
= 2        10
= 2        A
(101010)₂ = (2A)₁₆
(101010)₂ = (1 x 2⁵) + ( 0 x 2⁴) + (1 x 2³) + (0 x 2²) + ( 1x 2¹) + (0 x 2⁰)
= 32 + 0 + 8 + 0 + 2 + 0 = 42₁₀ 
(101010)₂ = (2A)₁₆ = 42₍₁₀₎

The number conversion is necessary because us enters the data into the computer in decimal form only and the computer is then expected to convert the decimal number to other number systems which it understands.

126₁₀

= 111111₂
= 1111110₂ = ?₈
= \(\overline { \underset { \overset { \downarrow }{ 1 } }{ 11 } } \) \(\overline { \underset { \overset { \downarrow }{ 7 } }{ 111 } } \) \(\overline { \underset { \overset { \downarrow }{ 6 } }{ 110 } } \)= 178₈
=1111110₂ =?_{16
= \(\overline { \underset { \overset { \downarrow }{ \overset { 7 }{ \overset { \downarrow }{ 7} } } }{ 111 } } \) \(\overline { \underset { \overset { \downarrow }{ \overset { 14 }{ \overset { \downarrow }{ E } } } }{ 1100 } } \)
=}7E₁₆
=126₁₀ = 1111110₂ = 176₈ = 7E₁₆

255₁₀

= 11111111₂
= 11111111₂ = ?₈
= \(\overline { \underset { \overset { \downarrow }{ 3 } }{ 11 } } \) \(\overline { \underset { \overset { \downarrow }{ 7 } }{ 111 } } \) \(\overline { \underset { \overset { \downarrow }{ 7 } }{ 111 } } \)
=377₈
= 11111111₂ =?₁₆
= \(\overline { \underset { \overset { \downarrow }{ \overset { 15 }{ \overset { \downarrow }{ f } } } }{ 1111 } } \)  \(\overline { \underset { \overset { \downarrow }{ \overset { 15 }{ \overset { \downarrow }{ f } } } }{ 1111 } } \)
= ff₁₆
= 255₁₀ = 11111111₂ = 377₈ = ff₁₆