Which concept represents the encoding of negative numbers in binary using a fixed number of bits?

Which concept represents the encoding of negative numbers in binary using a fixed number of bits?

• A. Binary shift
• B. Readfile command
• C. Two's complement
• D. Writefile command

Answer: (C)

Two's complement is the encoding used to represent negative numbers when a fixed number of bits is available. In an n-bit system, the representable range goes from -2^(n-1) to 2^(n-1) - 1. The way a negative number is encoded is to take the binary of its absolute value, invert all bits, and then add one. This makes arithmetic uniform: adding a number and its opposite yields zero modulo 2^n, so the same addition circuitry handles both positive and negative values. For example, in 8 bits, -5 becomes 11111011, while +5 is 00000101; their sum is 00000000 with a carry out, which is discarded in fixed-width arithmetic. This scheme also means -1 is all ones, and -128 is 10000000 in 8 bits. Positive numbers are simply their ordinary binary representations. The other terms refer to operations or file handling, not to how numbers are encoded.

Two's complement is the encoding used to represent negative numbers when a fixed number of bits is available. In an n-bit system, the representable range goes from -2^(n-1) to 2^(n-1) - 1. The way a negative number is encoded is to take the binary of its absolute value, invert all bits, and then add one. This makes arithmetic uniform: adding a number and its opposite yields zero modulo 2^n, so the same addition circuitry handles both positive and negative values. For example, in 8 bits, -5 becomes 11111011, while +5 is 00000101; their sum is 00000000 with a carry out, which is discarded in fixed-width arithmetic. This scheme also means -1 is all ones, and -128 is 10000000 in 8 bits. Positive numbers are simply their ordinary binary representations. The other terms refer to operations or file handling, not to how numbers are encoded.