Chapter 2

# Chapter 2 - Chapter 2 Problem Solutions 2.1. Decimal 32 33...

This preview shows pages 1–8. Sign up to view the full content.

- 2.1 - Chapter 2 Problem Solutions 2.1. Decimal Binary Ternary Octal Hexadecimal 32 100000 1012 40 20 33 100001 1020 41 21 34 100010 1021 42 22 35 100011 1022 43 23 36 100100 1100 44 24 37 100101 1101 45 25 38 100110 1102 46 26 39 100111 1110 47 27 40 101000 1111 50 28 41 101001 1112 51 29 42 101010 1120 52 2A 43 101011 1121 53 2B 44 101100 1122 54 2C 45 101101 1200 55 2D 46 101110 1201 56 2E 47 101111 1202 57 2F 48 110000 1210 60 30 49 110001 1211 61 31 50 110010 1212 62 32

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
- 2.2 - 2.2. Decimal Quaternary Quinary Duodecimal 0 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 10 4 4 5 11 10 5 6 12 11 6 7 13 12 7 8 20 13 8 9 21 14 9 10 22 20 A 11 23 21 B 12 30 22 10 13 31 23 11 14 32 24 12 15 33 30 13 16 100 31 14 17 101 32 15 18 102 33 16 19 103 34 17 20 110 40 18 21 111 41 19 22 112 42 1A 23 113 43 1B 24 120 44 20 25 121 100 21 26 122 101 22 27 123 102 23 28 130 103 24 29 131 104 25 30 132 110 26 31 133 111 27
- 2.3 - 2.3. (a) 1 1 (b) 1111 (c) 11 11 1 1101 1001 1100.01 + 1001 _____ + 111 _____ + 101.11 ________ 10110 10000 10010.00 (d) 111 11 (e) 111 (f) 1 11 11.011 111.01 0.1110 + 10.111 _______ + 11.10 _______ +0.1011 ______ 110.010 1010.11 1.1001 2.4. (a) 00 (b) 001 (c) 0110 1 1 /1/01 1 /1 /0/01.1 1 /0 /0 /1 /.0 /0 - 110 ____ - 1011.0 _______ - 11.01 _______ 111 1110.1 101.11 (d) 0 0 (e) 01 0 (f) 0 1 1 /01/.01 1 /0 /0.11/01 1011 /.0 /0 - 10.10 ______ - 11.1010 ________ - 10.11 _______ 10.11 1.0011 1000.01 2.5. (a) 10111 (b) 11011 × 110 _____ × 1011 _____ 00000 11011 10111 11011 10111 ________ 00000 10001010 11011 _________ 100101001 (c) 1010 (d) 101.1 × 1.01 ____ × 11.01 _____ 10 10 1 011 000 0 00 00 1010 _______ 101 1 1100.10 1011 _________ 10001.111 2.6. (a) 10.1 ________ 110011 ____________ 1010)11001.0 10101)10000101111 -1010 ____ - 10101 ______ 101 0 11000 -101 0 _____ -10101 _____ 0 11111 -10101 _____ 10101 -10101 _____ 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
- 2.4 - 2.6. (continued) (c) 110.101 ___________ (d) 101 1.01 ____________ 110)100111.110 101.1 )111101.1 11 - 110 ____ -1011 ____ 111 10001 -110 ___ - 1011 _____ 11 1 110 1 -11 0 ____ -101 1 _____ 110 1 0 11 -110 ___ -1 0 11 ______ 0 0 2.7. (a) 1 1 (b) 11 1 (c) 120 2012.0 220.12 2/0 /1 /02 + 1102.1 _______ + 121.20 _______ -12121 _____ 10121.1 1112.02 211 (d) 012 1 (e) 120.21 (f) 12202 1 /2 /0 /02/.12 × 122 ______ × 21.2 _____ - 2121.20 ________ 1011 12 10211 1 2110.22 10111 2 12202 12021 _________ 102111 _________ 100221.02 1122000.1 (g) 210.2 _________ (h) 1 2.02 ___________ 1012)221200.1 212.1 )11111.2 12 -2101 ____ - 2121 _____ 1110 1220 2 -1012 ____ -1201 2 ______ 210 1 12 0 12 -210 1 _____ -12 0 12 _______ 0 0 2.8. (a) Quaternary a+b b 0123 a 00123 1 1 2 3 1:0 2 2 3 1:0 1:1 3 3 1:0 1:1 1:2 Notation: x:y denotes carry digit x and sum digit y.
- 2.5 - 2.8. (continued) a-b b 0123 a 0 0 1:3 1:2 1:1 1 1 0 1:3 1:2 2 2 1 0 1:3 33210 Notation: x:y denotes borrow digit x and difference digit y. a × b b a 00000 10123 2 0 2 1:0 1:2 3 0 3 1:2 2:1 Notation: x:y denotes carry digit x and product digit y. (b) Octal a+b b 01234567 a 001234567 1 1 2 3 4 5 6 7 1:0 2 2 3 4 5 6 7 1:0 1:1 3 3 4 5 6 7 1:0 1:1 1:2 4 4 5 6 7 1:0 1:1 1:2 1:3 5 5 6 7 1:0 1:1 1:2 1:3 1:4 6 6 7 1:0 1:1 1:2 1:3 1:4 1:5 7 7 1:0 1:1 1:2 1:3 1:4 1:5 1:6 Notation: x:y denotes carry digit x and sum digit y.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
- 2.6 - 2.8. (continued) a-b b 01234567 a 0 0 1:7 1:6 1:5 1:4 1:3 1:2 1:1 1 1 0 1:7 1:6 1:5 1:4 1:3 1:2 2 2 1 0 1:7 1:6 1:5 1:4 1:3 3 3 2 1 0 1:7 1:6 1:5 1:4 4 4 3 2 1 0 1:7 1:6 1:5 5 5 4 3 2 1 0 1:7 1:6 6 6 5 4 3 2 1 0 1:7 776543210 Notation: x:y denotes borrow digit x and difference digit y. a × b b a 000000000 101234567 2 0 2 4 6 1:0 1:2 1:4 1:6 3 0 3 6 1:1 1:4 1:7 2:2 2:5 4 0 4 1:0 1:4 2:0 2:4 3:0 3:4 5 0 5 1:2 1:7 2:4 3:1 3:6 4:3 6 0 6 1:4 2:2 3:0 3:6 4:4 5:2 7 0 7 1:6 2:5 3:4 4:3 5:2 6:1 Notation: x:y denotes carry digit x and product digit y.
- 2.7 - 2.8. (continued) (c) Hexadecimal a+b b 0123456789ABCDEF a 00123456789ABCDEF 1 1 2 3 4 5 6 7 8 9 A B C D E F 1:0 2 2 3 4 5 6 7 8 9 A B C D E F 1:0 1:1 3 3 4 5 6 7 8 9 A B C D E F 1:0 1:1 1:2 4 4 5 6 7 8 9 A B C D E F 1:0 1:1 1:2 1:3 5 5 6 7 8 9 A B C D E F 1:0 1:1 1:2 1:3 1:4 6 6 7 8 9 A B C D E F 1:0 1:1 1:2 1:3 1:4 1:5 7 7 8 9 A B C D E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 8 8 9 A B C D E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 9 9 A B C D E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 A A B C D E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 B B C D E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 1:A C C D E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 1:A 1:B D D E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 1:A 1:B 1:C E E F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 1:A 1:B 1:C 1:D F F 1:0 1:1 1:2 1:3 1:4 1:5 1:6 1:7 1:8 1:9 1:A 1:B 1:C 1:D 1:E Notation: x:y denotes carry digit x and sum digit y.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 10/26/2010 for the course ENEE 244 taught by Professor Petrov during the Spring '08 term at Maryland.

### Page1 / 34

Chapter 2 - Chapter 2 Problem Solutions 2.1. Decimal 32 33...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online