What is meant by number base?

Answer 1

Image the number 1011

You would be tempted to say that it is one thousand and eleven because we are used to the decimal base system. Thr number is really equivalent to

1 x (10)^3 + 0 x (10)^2 + 1 x (10)^1 + 1 x (10)^0

Given that any number raised to zero power is 1, the above expression eavalutes to

1000 + 0 + 10 + 1 = 1011

Because we are used to the decimal system, we assume that the base is 10. Once you start dealing with computers which think in terms of binary numbers (base 2), the above number evaluates to

1 x (2)^3 + 0 x (2)^2 + 1 x (2)^1 + 1 x (2)^0

1 x 8 + 0 x 4 + 1 x 2 + 1 x 1 = 11 (the decimal equivalent)

As an exercise imagine that the number 1011 is in base 16 (hexadecimal) and in base 8 (octal) and evaluate the values. The answers should be 4113 and 521 respectively.

Observe that in base ten you have ten primitive symbols 0,1,2,3,4,5,6,7,8,9 and the base itself is formed by the combination of two primitive symbols, namely1 and0 to make 10 (decimal 10)

Inbasetwo you havetwo primitive symbols 0,1 and the base itself is formed by the combination of two primitive symbols, namely1 and0 to make 10(decimal 2)

In basesisxteen you have sixteen primitive symbols 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F and the base itself is formed by the combination of two primitive symbols, namely1 and0 to make 10 (decimal 16)

In base eight you haveeight primitive symbols 0,1,2,3,4,5,6,7 and the base itself is formed by the combination of two primitive symbols, namely1 and0 to make 10 (decimal 8)