2. A 4-bit comparator has inputs A = 1101 and B = 1011. Complete the table below. gti Iti eqi Digit 3 gto Ito eqo gti Iti eqi Digit 2 gto Ito eqo gti Iti eqi Digit 1 gto Ito eqo gti eqi Digit 0 gto Ito eqo

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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**Problem 2: 4-bit Comparator Explanation**

A 4-bit comparator is used to compare two binary numbers, each having 4 bits. In this example, the inputs are given as A = 1101 and B = 1011. The task is to complete the table that evaluates the comparison of each corresponding bit from two binary numbers.

**Table Explanation**

The table is divided into four columns labeled "Digit 3" to "Digit 0," representing each bit in the 4-bit number, starting from the most significant bit (MSB) to the least significant bit (LSB).

For each digit, the table includes three rows:
- **gti (greater than indicator):** Indicates whether the bit of A is greater than the corresponding bit of B.
- **lti (less than indicator):** Indicates whether the bit of A is less than the corresponding bit of B.
- **eqi (equals indicator):** Indicates whether the bit of A is equal to the corresponding bit of B.

**Column Explanation**

- **Digit 3:**
  - A = 1, B = 1
  - `gti`: No (0), since 1 is equal to 1
  - `lti`: No (0), since 1 is equal to 1
  - `eqi`: Yes (1), since both bits are 1

- **Digit 2:**
  - A = 1, B = 0
  - `gti`: Yes (1), since 1 is greater than 0
  - `lti`: No (0)
  - `eqi`: No (0)

- **Digit 1:**
  - A = 0, B = 1
  - `gti`: No (0)
  - `lti`: Yes (1), since 0 is less than 1
  - `eqi`: No (0)

- **Digit 0:**
  - A = 1, B = 1
  - `gti`: No (0)
  - `lti`: No (0)
  - `eqi`: Yes (1)

This table enables users to examine the comparison of each bit pair individually to understand how the 4-bit comparator evaluates the inputs A and B.
Transcribed Image Text:**Problem 2: 4-bit Comparator Explanation** A 4-bit comparator is used to compare two binary numbers, each having 4 bits. In this example, the inputs are given as A = 1101 and B = 1011. The task is to complete the table that evaluates the comparison of each corresponding bit from two binary numbers. **Table Explanation** The table is divided into four columns labeled "Digit 3" to "Digit 0," representing each bit in the 4-bit number, starting from the most significant bit (MSB) to the least significant bit (LSB). For each digit, the table includes three rows: - **gti (greater than indicator):** Indicates whether the bit of A is greater than the corresponding bit of B. - **lti (less than indicator):** Indicates whether the bit of A is less than the corresponding bit of B. - **eqi (equals indicator):** Indicates whether the bit of A is equal to the corresponding bit of B. **Column Explanation** - **Digit 3:** - A = 1, B = 1 - `gti`: No (0), since 1 is equal to 1 - `lti`: No (0), since 1 is equal to 1 - `eqi`: Yes (1), since both bits are 1 - **Digit 2:** - A = 1, B = 0 - `gti`: Yes (1), since 1 is greater than 0 - `lti`: No (0) - `eqi`: No (0) - **Digit 1:** - A = 0, B = 1 - `gti`: No (0) - `lti`: Yes (1), since 0 is less than 1 - `eqi`: No (0) - **Digit 0:** - A = 1, B = 1 - `gti`: No (0) - `lti`: No (0) - `eqi`: Yes (1) This table enables users to examine the comparison of each bit pair individually to understand how the 4-bit comparator evaluates the inputs A and B.
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