SECTION 2-2 Binary Numbers
5. Convert the following binary numbers to decimal:
(a) 11
(b) 100
(c) 111
(d) 1000
(e) 1001
(f) 1100
(g) 1011
(h) 1111
6. Convert the following binary numbers to decimal:
(a) 1110
(b) 1010
(c) 11100
(d) 10000
(e) 10101
(f) 11101
(g) 10111
(h) 11111
7. Convert each binary number to decimal:
(a) 110011.11
(b) 101010.01
(c) 1000001.111
(d) 1111000.101
(e) 1011100.10101
(f) 1110001.0001
(g) 1011010.1010
(h) 1111111.11111
8. What is the highest decimal number that can be represented by each of the following numbers of binary digits (bits)?
(a) two
(b) three
(c) four
(d) five
(e) six
(f) seven
(g) eight
(h) nine
(i) ten
(j) eleven
9. How many bits are required to represent the following decimal numbers?
(a) 17
(b) 35
(c) 49
(d) 68
(e) 81
(f) 114
(g) 132
(h) 205
10. Generate the binary sequence for each decimal sequence:
(a) 0 through 7
(b) 8 through 15
(c) 16 through 31
(d) 32 through 63
(e) 64 through 75
SECTION 2-3 Decimal-to-Binary Conversion
11. Convert each decimal number to binary by using the sum-of-weights method:
(a) 10
(b) 17
(c) 24
(d) 48
(e) 61
(f) 93
(g) 125
(h) 186
12. Convert each decimal fraction to binary using the sum-of-weights method:
(a) 0.32
(b) 0.246
(c) 0.0981
13. Convert each decimal number to binary using repeated division by 2:
(a) 15
(b) 21
(c) 28
(d) 34
(e) 40
(f) 59
(g) 65
(h) 73
14. Convert each decimal fraction to binary using repeated multiplication by 2:
(a) 0.98
(b) 0.347
(c) 0.9028
SECTION 2-4 Binary Arithmetic
15. Add the binary numbers:
(a) 11 + 01
(b) 10 + 10
(c) 101 + 11
(d) 111 + 110
(e) 1001 + 101
(f) 1101 + 1011
16. Use direct subtraction on the following binary numbers:
(a) 11 - 1
(b) 101 - 100
(c) 110 - 101
(d) 1110 - 11
(e) 1100 - 1001
(f) 11010 - 10111
17. Perform the following binary multiplications:
(a) 11 x 11
(b) 100 x 10
(c) 111 x 101
(d) 1001 x 110
(e) 1101 x 1101
(f) 1110 x 1101
18. Divide the binary numbers as indicated:
(a) 100 $div$ 10
(b) 1001 $div$ 11
(c) 1100 $div$ 100
SECTION 2-5 1's and 2's Complements of Binary Numbers
19. Determine the 1's complement of each binary number:
(a) 101
(b) 110
(c) 1010
(d) 11010111
(e) 1110101
(f) 00001
20. Determine the 2's complement of each binary number using either method:
(a) 10
(b) 111
(c) 1001
(d) 1101
(e) 11100
(f) 10011
(g) 10110000
(h) 00111101
SECTION 2-6 Signed Numbers
21. Express each decimal number in binary as an 8-bit sign-magnitude number:
(a) +29
(b) -85
(c) +100
(d) -123
22. Express each decimal number as an 8-bit number in the 1's complement form:
(a) -34
(b) +57
(c) -99
(d) +115
23. Express each decimal number as an 8-bit number in the 2's complement form:
(a) +12
(b) -68
(c) +101
(d) -125