Figure 4-75 represents a relative-magnitude detector that takes two three-bit binary numbers, x₂x₁x₀ and y₂y₁y₀, and determines whether they are equal and, if not, which one is larger. There are three outputs, defined as follows:

1. M = 1 only if the two input numbers are equal.

2. N = 1 only if x₂x₁x₀ is greater than y₂y₁y₀.

3. P = 1 only if y₂y₁y₀ is greater than x₂x₁x₀.

Design the logic circuitry for this detector. The circuit has six inputs and three outputs and is therefore much too complex to handle using the truth table approach. Refer to Example 4-17 as a hint about how you might start to solve this problem.

Figure 4-75

Data from Example 4-17

The notation x₁x₀ represents a two-bit binary number that can have any value (00, 01, 10, or 11); for example, when x₁ = 1 and x₀ = 0, the binary number is 10, and so on. Similarly, y₁y₀ represents another two-bit binary number. Design a logic circuit, using x₁, x₀, y₁, and y₀ inputs, whose output will be HIGH only when the two binary numbers x₁x₀ and y₁y₀ are equal.

Transcribed Image Text:

Binary X₂ number X₁ X Xo Binary number y Y2 Y₁ Yo LSB LSB Relative magnitude detector -M N { x =y] {x>y) P {x