Computer Number Systems: Decimal, Hexadecimal, Binary Conversion

This assignment provides solutions to problems related to computer number systems. It includes creating a table to count from 0 to 15 in decimal, hexadecimal, and binary formats, filling in a table for logical operations (AND, OR, XOR) with true and false inputs, and converting numbers between decimal, binary, and hexadecimal systems. The assignment also covers performing binary arithmetic operations such as addition, subtraction, and multiplication. Additionally, it includes directly converting a hexadecimal number to binary and decoding an ASCII string to reveal a message. The detailed steps for each conversion and operation are shown, offering a comprehensive understanding of number system concepts. Desklib offers more solved assignments and study tools for students.

Running head: COMPUTER NUMBER SYSTEM
COMPUTER NUMBER SYSTEM
Name of the Student
Name of the University
Author note

Table of Contents
Question 1............................................................................................................................3
Question 2............................................................................................................................4
Question 3............................................................................................................................5
Question 4............................................................................................................................7
Question 5............................................................................................................................9
Question 6..........................................................................................................................11
Question 7..........................................................................................................................13
Question 8..........................................................................................................................13

Question 1
Decimal Hexadecimal Binary
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000

9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
Question 2
X Y X
AND Y
X OR
Y
X
XOR Y
T T T T F
T F F T T

F T F T T
F F F F F
Question 3
Convert the following numbers from decimal to binary. Please show work.
 16:
Result: 10000
Process:
16 2
-16 8 2
0 -8 4 2
0 -4 2 2
0 -2 1
0
 165:
Result: 10100101
Steps:
165 2
-
164 82 2
1 -82 41 2

0 -40 20 2
1 -20 10 2
0 -10 5 2
0 -4 2 2
1 -2 1
0
 255:
Result: 11111111
Steps:
255 2
-
254 127 2
1 -
126 63 2
1 -62 31 2
1 -30 15 2
1 -14 7 2
1 -6 3 2
1 -2 1
1
 256
Result: 100000000
Steps:
256 2
- 128 2

256
0 -
128 64 2
0 -64 32 2
0 -32 16 2
0 -16 8 2
0 -8 4 2
0 -4 2 2
0 -2 1
0
 1243
Result: 10011011011
Process:
124
3 2
-
124
2
621 2
1 -
620 310 2
1 -
310 155 2
0 -
154 77 2
1 -76 38 2
1 -38 19 2
0 -18 9 2
1 -8 4 2
1 -4 2 2
0 -2 1
0

Question 4
 66
Result: 42
Process:
66 16
-64 4
2
 560
Result: 230
Process:
560 16
-
560 35 16
0 -32 2
3
 1001
Result: 3E9
Steps:
100
1 16
-992 62 16
9 -48 3
14=E

 15
Result: F
 199
Result: C7
Process:
199 16
-
192 12
7
Question 5
1. 133 (decimal) to hexadecimal
Answer: (10000101)
Whole part of a number is obtained by dividing on the basis new
133 2
-
132 66 2
1 -66 33 2
0 -32 16 2
1 -16 8 2
0 -8 4 2
0 -4 2 2
0 -2 1
0

2. 12AF (hexadecimal) to decimal to binary
Decimal: 4783
Steps: 12AF16 = 1∙163+2∙162+10∙161+15∙160 = 4096+512+160+15 = 478310
Binary: 1001010101111
Steps:
478
3 2
-
478
2
2391 2
1 -
2390 1195 2
1 -
1194 597 2
1 -
596 298 2
1 -
298 149 2
0 -
148 74 2
1 -74 37 2
0 -36 18 2
1 -18 9 2
0 -8 4 2
1 -4 2 2
0 -2 1
0
3. 1110111 (binary) to decimal to hexadecimal
Decimal: 119
Steps: 11101112 = 1∙26+1∙25+1∙24+0∙23+1∙22+1∙21+1∙20 = 64+32+16+0+4+2+1 = 11910

Hexadecimal: 77
Steps:
119 16
-
112 7
7
4. 11010101 (binary) to decimal
Decimal: 213
Steps: 110101012 = 1∙27+1∙26+0∙25+1∙24+0∙23+1∙22+0∙21+1∙20 = 128+64+0+16+0+4+0+1
= 21310
5. 32CF (hexadecimal) to decimal to binary
Decimal: 13007
Steps: 32CF16 = 3∙163+2∙162+12∙161+15∙160 = 12288+512+192+15 = 1300710
Binary: 11001011001111
Steps:
1300
7 2
-
1300
6
6503 2
1 - 3251 2

6502
1 -
3250 1625 2
1 -
1624 812 2
1 -
812 406 2
0 -
406 203 2
0 -
202 101 2
1 -
100 50 2
1 -50 25 2
0 -24 12 2
1 -12 6 2
0 -6 3 2
0 -2 1
1
Question 6
Binary Addition
1. 110+110
Result: 1100
Process: Number 1 in the decimal system
1102 = 610
Number 2 in the decimal system
1102 = 610
Their sum

6 + 6 = 12
Result in binary form
1210 = 11002
2. 10101+111
Result: 11100
Process: Number 1 in the decimal system
101012 = 2110
Number 2 in the decimal system
1112 = 710
Their sum
21 + 7 = 28
Result in binary form
2810 = 111002
3. 110 – 11
Result: 11
Process: Number 1 in the decimal system
1102 = 610
Number 2 in the decimal system

112 = 310
Their difference is
6 - 3 = 3
Result in binary form
310 = 112
4. 1001 – 11
Result: 110
Process
Number 1 in the decimal system
10012 = 910
Number 2 in the decimal system
112 = 310
Their difference is
9 - 3 = 6
Result in binary form
610 = 1102
5. 100 x 11
Result: 1100

Process
Number 1 in the decimal system
1002 = 410
Number 2 in the decimal system
112 = 310
Their product
4 * 3 = 12
Result in binary form
1210 = 11002
Question 7
Directly convert F8 (hexadecimal) to binary (without first converting to decimal).
248
Question 8
1. What does the following string say? You can use the ASCII PowerPoint slide in the Engage
course shell for help.
74—68—69—73—20—69—73—20—61—20—74—65—73—74
Answer: this is a test