Binary Arithmetic and Signed Numbers

These flashcards cover key vocabulary related to binary arithmetic, signed numbers, and their representations in digital systems.

Binary Arithmetic

A system of arithmetic that uses only two digits, 0 and 1, essential for digital computers.

1’s Complement

A binary number system where all 1s are changed to 0s and all 0s are changed to 1s.

2’s Complement

A method of representing negative numbers in binary by taking the 1’s complement and adding 1.

Sign Bit

The left-most bit in a signed binary number indicating whether the number is positive (0) or negative (1).

Sign-Magnitude

A binary representation where the leftmost bit is the sign bit and the remaining bits represent the magnitude.

Binary Addition

The arithmetic operation of adding binary numbers where 1 + 1 results in 10.

Binary Subtraction

The operation of subtracting one binary number from another, where 10 - 1 = 1.

Binary Multiplication

The process of multiplying binary numbers, similar to decimal multiplication but with bits.

Binary Division

The operation of dividing binary numbers, which can be computed with a calculator.

Magnitude Bits

The bits in a binary representation that indicate the absolute value of the number, excluding the sign.

Negative Number Representation

In binary systems, negative numbers can be represented using sign-magnitude, 1’s complement, or 2’s complement.

Decimal Value of Signed Numbers

Calculated by summing weights of the magnitude bits where there are 1s and assigning negative values to the sign bit.

Positive Numbers in 2’s Complement

Same as in sign-magnitude and 1’s complement forms, represented as the binary equivalent of the value.

Converting from Complement to True Binary

For 1’s complement, reverse all bits; for 2’s complement, take 1’s complement and add 1.

Arithmetic Operations in Binary

Fundamental operations include addition, subtraction, multiplication, and division performed in binary format.

Least Significant Bit (LSB)

The right-most bit in a binary number, significant for determining value in arithmetic operations.