Binary number is a number expressed in the base 2 numeral system. Binary number's digits have 2 symbols: zero (0) and one (1). Each digit of a binary number counts a power of 2.
Binary number example:
11012 = 1×23+1×22+0×21+1×20 = 1310
Decimal number is a number expressed in the base 10 numeral system. Decimal number's digits have 10 symbols: 0,1,2,3,4,5,6,7,8,9. Each digit of a decimal number counts a power of 10.
Decimal number example:
65310 = 6×102+5×101+3×100
For binary number with n digits:
dn-1 ... d3 d2 d1 d0
The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):
decimal = d0×20 + d1×21 + d2×22 + ...
Find the decimal value of 1110012:
binary number: | 1 | 1 | 1 | 0 | 0 | 1 |
---|---|---|---|---|---|---|
power of 2: | 25 | 24 | 23 | 22 | 21 | 20 |
1110012 = 1⋅25+1⋅24+1⋅23+0⋅22+0⋅21+1⋅20 = 5710
Binary Number |
Decimal Number |
Hex Number |
---|---|---|
0 | 0 | 0 |
1 | 1 | 1 |
10 | 2 | 2 |
11 | 3 | 3 |
100 | 4 | 4 |
101 | 5 | 5 |
110 | 6 | 6 |
111 | 7 | 7 |
1000 | 8 | 8 |
1001 | 9 | 9 |
1010 | 10 | A |
1011 | 11 | B |
1100 | 12 | C |
1101 | 13 | D |
1110 | 14 | E |
1111 | 15 | F |
10000 | 16 | 10 |
10001 | 17 | 11 |
10010 | 18 | 12 |
10011 | 19 | 13 |
10100 | 20 | 14 |
10101 | 21 | 15 |
10110 | 22 | 16 |
10111 | 23 | 17 |
11000 | 24 | 18 |
11001 | 25 | 19 |
11010 | 26 | 1A |
11011 | 27 | 1B |
11100 | 28 | 1C |
11101 | 29 | 1D |
11110 | 30 | 1E |
11111 | 31 | 1F |
100000 | 32 | 20 |
1000000 | 64 | 40 |
10000000 | 128 | 80 |
100000000 | 256 | 100 |