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.