Section 5
PROBLEMS
SECTIONS 21 AND 22
21 Convert these binary numbers to decimal.
 10110
 10001101
 100100001001
 1111010111
 10111111
22 Convert the following decimal values to binary.
 37
 14
 189
 205
 2313
 511
23 what is the largest decimal value that can be represented by an 8bit binary number? A 16bit number?
SECTION 23
24 Convert each octal number to its decimal equivalent.
 743
 36
 3777
 257
 1204
25 Convert each of the following decimal numbers to octal.
 59
 372
 919
 65,536
 255
26 Convert each of the octal values from Problem 24 to binary.
27 Convert the binary numbers in Problem 21 to octal.
28 List the binary numbers in Problem 21 to octal.
29 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 22(e).
SECTION 24
210 Convert these hex values to decimal.
 92
 1A6
 37FD
 2CO
 7FF
211 Convert these decimal values to hex.
 75
 314
 2048
 25,619
 4095
212 Convert the binary numbers in Problem 21 to hexadecimal.
213 Convert the hex values in problem 210 to binary.
214 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 8bit 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?
215 List the hex numbers in sequence from 280 to 2A0.
SECTION 25
216 Encode these decimal numbers in BCD
 47
 962
 187
 42,689,627
 1204
How many bits are required to represent the decimal numbers in the range from 0 to 999 using straight binary code? Using BCD code?
218 The following numbers are in BCD. Convert them to decimal.
 1001011101010010
 000110000100
 0111011101110101
 010010010010
SECTION 28
219 Represent the statement “X=25/Y” in ASCII code (excluding quotes). Attach an evenparity bit.
220 Attach an evenparity bit to each of the ASCII codes for problem 219 and give the results in hex.
221 The following code groups are being transmitted. Attach an evenparity bit to each group.
 10110110
 00101000
 11110111
SECTION 29
222 Convert the following decimal numbers to BCD code and then attach an oddparity bit.
 74
 38
 165
 9201
223. In a certain digital system, the decimal numbers from 000 through 999 are represented in BCD code. An oddparity 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.)
 1001010110000
 0100011101100
 0111110000011
 1000011000101
224 Suppose that the receiver received the following data from the transmitter of Example 210.
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?
DRILL QUESTIONS
225 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 binarytodecimal conversion may be done directly, or it may be done as a binarytooctal conversion followed by an octaltodecimal conversion.
DRILL QUESTIONS
225. 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 binarytodecimal conversion may be done directly, or it may be done as a binarytooctal conversion followed by an octaltodecimal conversion.
 1417=____________
 255 =____________
 11010001=________
 11101010000100111=______________
 111010110000100111=_____________
 2497=____________
 511=_____________
 235=_____________
 4316=____________
 7A9=_____________
 3E1c=____________
 1600=____________
 38,187=___________
 865=_____________(BCD)
 10010100011 (BCD)=__________
 465=_____________
 B34=_____________
 01110100(BCD)=_____________
 111010=__________(BCD)
226. Represent the decimal value 37 in each of the following ways.
 straight binary
 BCD
 Hex
 ASCII
 Octal
227 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 4bit 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.
228. Write to binary number that results when each of the following numbers is incremented by one: (a) 0111 (b) 010000 (c) 1110
229. Repeat Problem 228 for the decrement operation.
230. Write the number that results when each of the following is incremented:
 7777
 7777
 2000
 2000
 9FF
 1000
231. Repeat problem 230 for the decrement operation.
CHALLENGING EXERCISES
232. Perform the following conversions between base5 and decimal
 3421=___________
 726 =___________
233 Convert the following binary number directly into its base4 equivalent: 01001110
234 Construct a table showing the binary, octal, hex and BCD representations of all decimal numbers from 0 to 15. Compare your table with Table 23.
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