-101
87
1111 degrees 1111 degrees 1111 degrees
The binary sequence for the numbers 8 through 15 in decimal form are as follows: 8 is 1000, 9 is 1001, 10 is 1010, 11 is 1011, 12 is 1100, 13 is 1101, 14 is 1110, 15 is 1111. In binary, each digit represents a power of 2 starting from the rightmost position with 2^0, then 2^1, 2^2, and so on.
Each hexadecimal digit (or nybble) is the equivalent of 4 binary digits (or bits) with a decimal value of 0-15. Convert each nybble into (4) binary (digits) and string them together, remembering the conversion of decimal 0-15 to binary: Hex -> Dec -> Binary 0 -> 00 -> 0000 1 -> 01 -> 0001 2 -> 02 -> 0010 3 -> 03 -> 0011 4 -> 04 -> 0100 5 -> 05 -> 0101 6 -> 06 -> 0110 7 -> 07 -> 0111 8 -> 08 -> 1000 9 -> 09 -> 1001 A -> 10 -> 1010 B -> 11 -> 1011 C -> 12 -> 1100 D -> 13 -> 1101 E -> 14 -> 1110 F -> 15 -> 1111 So to convert 0x6AF to binary: 6 -> 0110 A -> 1010 F -> 1111 => 0x6AF = 0110 1010 1111 = 011010101111 (without the spaces showing the hex nybbles)
542AM the next day
1010 base 2 = 10 base 10 1010 base 10 = 11 1111 0010 base 2
87
detects the invalid portion of the bcd number codes (1010-1111)
101, 202, 303, 404, 505, 606, 707, 808, 909, 1010, 1111, . . .
It is 5 hours:9-1010-1111-1212-11-2
101
The 1's complement is formed by inverting every binary digit (bit) of the number - if it is a 0 it becomes a 1, otherwise it is a 1 and becomes a 0. If 10 is in base 2, then its 1's compliment is 01 or just 1. If 10 is in base 10, then in binary it is 1010 and its 1's complement is 0101 = 5 in decimal. However, if more bits are being used to store it, there would be leading 0s that get inverted to 1s and so the resultant number is different; examples: 8 bits (a byte): decimal 10 = 0000 1010 → 1111 0101 = 245 in decimal 16 bits: decimal 10 = 0000 0000 0000 1010 → 1111 1111 1111 0101 = 65525 Next, if 2s complement is being used to represent negative numbers, the binary 1111 0101 represents decimal -11; similarly 1111 1111 1111 0101 represents decimal -11.
101, 202, 303, 404, 505, 606, 707, 808, 909, 1010, 1111, 1212
The answer is 1 0101 0111 1110 1011 1011 0011 1111 1010 0001 0111
1 + 1,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111 = 1,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,112 Unless it is binary, in which case: 1 + 111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 11111 1111 1111 1111 1111 = 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
They are, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111.
10 = 1010, 11 = 1011, 12 = 1100, 13 = 1101, 14 = 1110, 15 = 1111, 16 = 10000.