Question

Convert the following numbers from their initial radix into the other two common representation (Decimal, Hex, Binary):

1. 0b10010011
2. 0xD3AD
3. 63
4. 0b00100100
5. 0xB33F
6. 0
7. 39
8. 0x7EC4

Answer 1

To convert numbers from one representation to another (radix conversion), we can use the place value system and conversions specific to each radix. For example, binary to decimal conversion can be done using the place value system, while decimal to hexadecimal conversion involves dividing the decimal number by 16 and tracking the remainders. Converting hexadecimal to binary requires converting each hexadecimal digit to its binary equivalent.

Step-by-step explanation:

To convert numbers from one representation to another (radix conversion), we can use the following conversions:

• To convert from binary to decimal, we can use the place value system.
• To convert from decimal to hexadecimal, we can divide the decimal number by 16 and keep track of the remainders. The remainders will be the hexadecimal digits.
• To convert from hexadecimal to binary, we can convert each hexadecimal digit to its binary equivalent.

Using these conversions, we can convert the given numbers:

1. 0b10010011 in decimal is 147 and in hexadecimal is 0x93.
2. 0xD3AD in decimal is 53613 and in binary is 0b1101001110101101.
3. 63 in decimal is 0x3F and in binary is 0b111111.
4. 0b00100100 in decimal is 36 and in hexadecimal is 0x24.
5. 0xB33F in decimal is 45951 and in binary is 0b1011001100111111.
6. 0 in decimal is 0 and in hexadecimal is 0x0.
7. 39 in decimal is 0x27 and in binary is 0b100111.
8. 0x7EC4 in decimal is 32452 and in binary is 0b1111111011000100.