The digital computer is such a versatile piece of technology because it can be used in a
staggering amount of different applications with the use of programs, sets of instructions that
operate on inputs and return outputs. Anything that can be represented concretely and
numerically is fair game for a computer. This data is encoded through different voltage ranges,
named HIGH and LOW. The nature of only having two possible states gives a low margin for
error, and makes it so random noise variations in the strength of the voltage don’t have as severe
an effect on the integrity of the signal. The inside of a computer’s processor contains millions of
transistors, which can each hold a high or low voltage value.
In order to turn information into combinations of high and low signals, we use binary
numbers. Everyday decimal numbers are base 10, meaning that there are unique symbols for the
first 10 numbers. Binary differs from this in that there are only two possible digits, 0 and 1.
These can be correlated to high and low voltages within the CPU to express numbers, and
therefore everything that follows. Computers also use octal and hexadecimal (base 8 and 16) at
higher levels due to how easy they are to convert back to binary.
Q1-2: 12 kilobits = 12000 bits, 128 megabits = 1.28 * 10^8 bits, 2 gigabits = 2*10^9 bits
Q1-3: The largest binary number expressible with n digits is 2^n – 1, so 8 bits can express up to
255 unique values, and 32 bits can express up to 4294967295 values.
Q1-4: 111010 -> 58, 10101111.101 ->175.625, 110110110 -> 438.