Question

Based on your results in Problems 4-1 and 4-2, which is more efficient in expressing decimal numbers in the fewest number of bits, binary or BCD? Why is the less efficient coding scheme still very useful?

Short answer

The binary expression of a decimal number is more efficient than its BCD expression. Still, BCD is used due to its ease of conversion to decimal and it is easy to implement its circuitry.

Step-by-step solution

Step 1. Introduction

A decimal number can be converted into its binary equivalent by dividing the decimal number by 2 repeatedly and recording the remainders. The remainders are then written from top to bottom to get the equivalent binary number.

The BCD equivalent of a decimal number is obtained by replacing all the digits of the given decimal number with their corresponding BCD equivalents.

Step 2. Explanation

The BCD and the binary equivalent of the given decimal numbers along with the number of bits can be represented in a table.

Decimal Number	Binary	BCD	Number of Bits in Binary	Number of Bits in BCD
37	100101	00110111	6	8
93	1011101	10010011	7	8
129	10000001	00100101001	8	12
355	101100011	001101010101	9	12

Here, we can clearly see that the BCD system has more bits than the binary equivalent.

So, binary is more efficient compared to BCD. But BCD is widely used as it is easier to convert a decimal to BCD. Also, BCD is easier to use in digital circuit systems.