SECTIONS 2-1 AND 2-2
2-1 Convert these binary numbers to decimal.
2-2 Convert the following decimal values to binary.
2-3 what is the largest decimal value that can be represented by an 8-bit binary number? A 16-bit number?
2-4 Convert each octal number to its decimal equivalent.
2-5 Convert each of the following decimal numbers to octal.
2-6 Convert each of the octal values from Problem 2-4 to binary.
2-7 Convert the binary numbers in Problem 2-1 to octal.
2-8 List the binary numbers in Problem 2-1 to octal.
2-9 When a large decimal number is to be converted to binary, it is sometimes easier to convert it first to octal, and then from octal to binary. Try this procedure for 2313 and compare it with the procedure used in problem 2-2(e).
2-10 Convert these hex values to decimal.
2-11 Convert these decimal values to hex.
2-12 Convert the binary numbers in Problem 2-1 to hexadecimal.
2-13 Convert the hex values in problem 2-10 to binary.
2-14 In most microcomputers the addresses of memory locations are specified in hexadecimal. These addresses are sequential numbers that identify each memory circuit.
- A particular microcomputer store an 8-bit number in each memory location. If the memory addresses range from 0000 to FFFF, how many memory locations are there?
- Another microcomputer is specified to have 4096 memory locations. What range of hex addresses does this computer use?
2-15 List the hex numbers in sequence from 280 to 2A0.
2-16 Encode these decimal numbers in BCD
How many bits are required to represent the decimal numbers in the range from 0 to 999 using straight binary code? Using BCD code?
2-18 The following numbers are in BCD. Convert them to decimal.
2-19 Represent the statement “X=25/Y” in ASCII code (excluding quotes). Attach an even-parity bit.
2-20 Attach an even-parity bit to each of the ASCII codes for problem 2-19 and give the results in hex.
2-21 The following code groups are being transmitted. Attach an even-parity bit to each group.
2-22 Convert the following decimal numbers to BCD code and then attach an odd-parity bit.
2-23. In a certain digital system, the decimal numbers from 000 through 999 are represented in BCD code. An odd-parity bit is also included at the of each code group. Examine each of the code groups below and assume that each one has just been transferred from one location to another. some of the groups contain errors. Assume taht no more than two errors have occured for each group. Determine which of the code groups have a single error and which of them definitely have a double error. (Hint: Remember that this is a BCD code.)
2-24 Suppose that the receiver received the following data from the transmitter of Example 2-10.
0 1 0 0 1 0 0 0
1 1 0 0 0 1 0 1
1 1 0 0 1 1 0 0
1 1 0 0 1 0 0 0
1 1 0 0 1 1 0 0
What errors can be the receiver determine in these received data?
2-25 Perform each of the following conversions. For some of them, you may want to try several methods to see which one works best for you. For example, a binary-to-decimal conversion may be done directly, or it may be done as a binary-to-octal conversion followed by an octal-to-decimal conversion.
2-25. Perform each of the following coversions. For some of them, you may want to try several methods to see which one works best for you. For example, a binary-to-decimal conversion may be done directly, or it may be done as a binary-to-octal conversion followed by an octal-to-decimal conversion.
- 255 =____________
- 10010100011 (BCD)=__________
2-26. Represent the decimal value 37 in each of the following ways.
- straight binary
2-27 Fill in the blanks with the correct word or words.
- Conversion from decimal to _______requires repeated division by 8.
- Conversion from decimal to hex requires repeated division by_______.
- In the BCD code, each___________ is converted to its 4-bit binary equivalent.
- The_________code has the characteristic that only one bit changes in going from one step to the next.
- A transmitter attaches a________to a code group to allow the receiver to detect_______.
- The__________code is the most common alphanumeric code used in computer systems.
- __________and_________are often used as a convenient way to represent large binary numbers.
2-28. Write to binary number that results when each of the following numbers is incremented by one: (a) 0111 (b) 010000 (c) 1110
2-29. Repeat Problem 2-28 for the decrement operation.
2-30. Write the number that results when each of the following is incremented:
2-31. Repeat problem 2-30 for the decrement operation.
2-32. Perform the following conversions between base-5 and decimal
- 726 =___________
2-33 Convert the following binary number directly into its base-4 equivalent: 01001110
2-34 Construct a table showing the binary, octal, hex and BCD representations of all decimal numbers from 0 to 15. Compare your table with Table 2-3.