what are decimal equivalent of hexa decimal number a b c d e f ?
Answers
Answer:
Since number numbers are type of positional number system. That means weight of the positions from right to left are as 160, 161, 162, 163and so on. for the integer part and weight of the positions from left to right are as 16-1, 16-2, 16-3and so on. for the fractional part.
You can directly convert a hexadecimal number into decimal number using reverse method of decimal to hexadecimal number.
Assume any unsigned hexadecimal number is hnh(n-1) ... h1h0.h-1h-2 ... h(m-1)hm. Then the decimal number is equal to the sum of hexadecimal digits (hn) times their power of 16 (16n), i.e.,
= hnh(n-1) ... h1h0.h-1h-2 ... h(m-1)hm
= hnx16n+h(n-1)x16(n-1)+ ... +h1x161+h0x160+h-1x16-1+h-2x16-2+ ... +h(m-1)x16-(m-1)+h-mx16-m
This is simple algorithm where you have to multiply positional value of binary with their digit and get the sum of these steps.
Example-1 − Convert hexadecimal number ABCDEF into decimal number.
Since value of Symbols − A, B, C, D, E, F are 10, 11, 12, 13, 14, 15 respectively. Therefore equivalent decimal number is,
= (ABCDEF)16 = (10x165+11x164+12x163+13x162+14x161+15x160)10
= (10485760+720896+49152+3328+224+15)10 = (11259375)10 which is answer.
Example-2 − Convert hexadecimal number 1F.01B into decimal number.
Since value of Symbols: B and F are 11 and 15 respectively. Therefore equivalent decimal number is,
= (1F.01B)16 = (1x161+15x160 +0x16-1+1x16-2+11x16-3)10 = (31.0065918)10 which is answer.