Question

In a full adder, which expression represents the carry generator?

a. g = abg=ab
b. g = a + bg=a+b
c. g = a \cdot bg=a⋅b
d. g = a - bg=a−b

Answer 1

The expression that represents the carry generator in a full adder is 'g = a \cdot b.' This indicates a carry is generated when both input bits a and b are 1, which is critical for accurate multi-bit binary addition.

Step-by-step explanation:

In a full adder - a digital circuit that adds binary numbers - the carry generator is the part of the circuit that determines if a carry bit should be included in the next significant bit position when adding two binary digits along with a carry from a less significant bit position. The correct expression for the carry generator in a full adder is g = a \cdot b, which means that the carry is generated when both inputs a and b are 1.

This concept is crucial in binary addition where the carry must be accounted for to ensure the correct sum is calculated across multiple-bit binary numbers. This choice of a carry generator guarantees that a carry is issued only when both bits a and b are high (binary 1), reflective of the binary addition rule where a carry is generated if both bits are 1 (1 + 1 = 0 with a carry of 1).