# Number Conversion: Hexadecimal to Binary, Binary Arithmetic, BCD Conversion

## How to convert hexadecimal number BC57 into binary?

Show the working steps.

## How to convert binary number 10101010010101 into hexadecimal?

Show the working steps.

## Perform the following binary arithmetic:

1) 10111 + 1001

2) 110101 - 11010

## Explain Binary-coded decimal (BCD) conversion.

Show the working steps.

1) Convert the decimal number 6370 into BCD.

2) Convert the BCD number 10010110010001 into decimal.

## Answer:

Number conversion between hexadecimal and binary involves converting a hexadecimal number to its binary equivalent or vice versa. Binary arithmetic involves performing addition or subtraction operations on binary numbers. Binary-coded decimal (BCD) conversion is a way of representing decimal numbers using binary digits.

## Hexadecimal to Binary Conversion:

To convert the hexadecimal number BC57 to binary, replace each hexadecimal digit with its 4-bit binary representation and combine the binary representations: BC57 = 1011 1100 0101 0111.

## Binary to Hexadecimal Conversion:

To convert the binary number 10101010010101 to hexadecimal, split the binary number into groups of 4 bits, replace each group of 4 bits with its hexadecimal equivalent, and combine the hexadecimal digits: 10101010010101 = AA55.

## Binary Arithmetic:

1) 10111 + 1001 = 100000

2) 110101 - 11010 = 99511

## BCD Conversion:

To convert the decimal number 6370 to BCD, replace each decimal digit with its 4-bit BCD code and combine the BCD codes: 6370 = 0110 0011 0111 0000.

To convert the BCD number 10010110010001 to decimal, split the BCD number into groups of 4 bits, replace each group of 4 bits with its decimal equivalent, and combine the decimal digits: 10010110010001 = 9641.