Computer Basics and Numerical Methods

Binary 1010.01 is calculated as (12^3) + (02^2) + (12^1) + (02^0) + (02^-1) + (12^-2) = 8 + 0 + 2 + 0 + 0 + 0.25 = 10.25.

Hexadecimal A1.4 is (1016^1) + (116^0) + (4*16^-1) = 160 + 1 + 0.25 = 161.25.

To convert 0.125 to hex, multiply by 16: 0.125 * 16 = 2.0. The integer part is 2, so the result is 0.2 in base 16.

Binary 100 is (12^2) + (02^1) + (0*2^0) = 4 + 0 + 0 = 4.

A computer executes instructions contained within a program. While programs are built using algorithms, the computer itself executes the compiled or interpreted program code.

In structured programming, basic control structures (sequence, selection, iteration) follow the single entry-single exit principle. This makes programs easier to understand, debug, and maintain. Note the typo exists should be exit.

The 'FOR-DO' construct (or a standard 'do-while' loop in many languages) is designed to execute the loop body at least once before checking the condition.

RAM is the standard acronym for Random Access Memory, which is the volatile memory used by a computer to store data currently in use.

The Central Processing Unit (CPU) is often referred to as the brain or heart of the computer because it performs the primary calculations and logic operations.

ROM stands for Read Only Memory, which is non-volatile memory used to store firmware or startup instructions.

A hard copy is a physical, printed version of information that exists in a digital format on a computer.

In 0.003050, leading zeros are not significant. The significant digits are 3, 0, 5, and 0. Thus, there are 4 significant digits.

LED is the standard acronym for Light Emitting Diode, a semiconductor device that emits light when current flows through it.

Rounding 3.68451 to three decimal places: the fourth decimal digit is 5, so we round up the third digit (4) to 5. The result is 3.685.

In the number 0.4, there is only one non-zero digit, making it the only significant digit.

Rounding 2.089 to three significant digits gives 2.09. The absolute error is the difference between the exact value and the rounded value, which is |2.089 - 2.09| = 0.001.

When rounding to n decimal places, the maximum absolute error is 0.5 * 10^-n. The relative error is bounded by (0.5 * 10^-n) / |x|. The provided formula in C is a common textbook approximation for this bound.

To round 0.0008857 to three significant digits, identify the first three non-zero digits (8, 8, 5). The next digit is 7, so round up the 5 to 6. The result is 0.000886.

In 20340, if the trailing zero is not significant (most common interpretation), significant digits are 2, 3, 4 (total 4). If it were significant, there would be 5.

The decimal number 7 is represented in binary as 111 because 12^2 + 12^1 + 1*2^0 = 4 + 2 + 1 = 7. Option B correctly identifies this binary representation.

A WHILE-DO loop checks the condition before executing the loop body. If the condition is false initially, the loop body executes zero times.

An algorithm is defined as a finite sequence of instructions to solve a problem, and it must produce at least one output to be useful.