410 = 1002
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The number of binary operations that can be defined on a set with 4 elements is 4^(4*4) = 4^16 = 4.294.967.296
4
The number 23 is 10111 in binary. The digits in a binary number are exponents of 2 rather than 10, so that for a five digit number in binary, the digit places represent 16, 8, 4, 2, 1 instead of increasing values of 10. 10111 = 16+0+4+2+1 = 23
The binary number 1000 is the decimal (base 10) number 8. The digits in a binary number are exponents of 2 rather than 10, so that for a four-digit number in binary, the digit places represent 8, 4, 2, 1 1000 (binary) = 8 + (0x4) + (0x2) + (0x1) = 8
11100 = 8192 + 2048 + 512 + 256 + 64 + 16 + 8 + 4 So 1110010 = 10,101,101,011,100 in binary.