From CDS 130
1. Powers of Two
1.1. Find the result of the following and provide the answer in power of two
2^{15} x 2^{13} x 2^{10}
1.2. Find the result of the following and provide the answer in power of two
( 2^{18} x 2^{12} ) / ( 2^{13} x 2^{7} )
2. Converting numbers between different bases
2.1. Convert (53)_{7} to hexdecimal (base 16) notation
2.2. Convert (BF)_{16} to binary
3. The template method
3.1. Using the template method, convert 101111_{2} to its decimal equivalent
1  0  1  1  1  1

2^{5}  2^{4}  2^{3}  2^{2}  2^{1}  2^{0}

?  ?  ?  ?  ?  ?

3.2. Using the template method, convert 227_{10} to its binary equivalent
3.3. Using the extended template method, convert 25.875_{10} to its binary equivalent
4. Binary representation of numbers
4.1. What is the binary (base 2) number 1001111011, written in decimal (base 10)?
4.2. What is the largest positive base 10 integer that can be represented with 10 bits?
4.3. How many different patterns of 1 and 0 can be produced using 10 bits?
4.4. How many bits are needed to represent the base10 number 1023 ?
4.5. How many bit patterns can be formed by 7 bits?
4.6. convert (198)_{10} to its binary equivalent
5. INTEGER MULTIPLICATION AND DIVISION OF BINARY NUMBERS BY POWERS OF TWO
5.1. Multiply 1101010101011_{2} by 8_{10} and represent the result in binary
5.2. Divide 111001011001010_{2} by 32_{10} and represent the result in binary
6. Binary Addition
6.1. Add (100101.110101)_{2} and (11.1101)_{2} . Express your result in binary
6.2. Add (1.625)_{10} and (0.5625)_{10} . Express your result in binary
7. Binary Multiplication
7.1. Multiply the binary numbers 0110111 and 1011
7.2. Calculate (111010101)_{2} multiplied by (1024)_{10} (without using a calculator), and represent the result in integer binary.