Chapter 87, Problem 1A

To determine

Conversion of decimal numbers 143.8₁₀ to a 2421 code numbers.

Answer to Problem 1A

2421 code numbers is 0001 0100 0011.1110.

Explanation of Solution

Given information:

A decimal numbers 143.8₁₀.

Calculation:

2421 code is also called Aiken code. It is a complementary BCD code.

2421 code number system uses 2 symbols: The numbers are 0 and 1.

And a decimal number system uses the number 10 as its base i.e. it has 10 symbols; decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

2421 code numbers are represented as from decimal number

Decimal	0	1	2	3	4	5	6	7	8	9
2421 code	0000	0001	0010	0011	0100	1011	1100	1101	1110	1111

Each decimal digit consists of 4 bits 2421 code.

For example, decimal number 9 is equal to 2421 code 1111.

For converting decimal numbers into 2421 code numbers, write down the decimal numbers and represent each decimal digit by its 2421 code from the table.

Then combine all the digits together.

Same process follows for integer as well as fractional part.

  $\begin{array}{l}decimalnumber={143.8}_{10}\\ Nowconsideringindividualdigits\\ decimaldigit=1\\ decimaldigit=0+0+0+1(summationintermsof2421)\\ decimaldigit=\overline{)0}\times 2+\overline{)0}\times 4+\overline{)0}\times 2+\overline{)1}\times 1\\ So2421code=\boxed{0001}\end{array}$

  $\begin{array}{l}decimaldigit=4\\ decimaldigit=0+4+0+0(summationintermsof2421)\\ decimaldigit=\overline{)0}\times 2+\overline{)1}\times 4+\overline{)0}\times 2+\overline{)0}\times 1\\ So2421code=\boxed{0100}\end{array}$

  $\begin{array}{l}decimaldigit=3\\ decimaldigit=0+0+2+1(summationintermsof2421)\\ decimaldigit=\overline{)0}\times 2+\overline{)0}\times 4+\overline{)1}\times 2+\overline{)1}\times 1\\ So2421code=\boxed{0011}\end{array}$

  $combineallthe2421codestogether=000101000011.1110$