Exercise 1.1.1 “2931” 2000 + 900 + 30 + 1 = 2931
Exercise 1.1.2 “110^2
2^2 2^1 2^0
4 2 1
X X X
1 1 0 4 + 2 + 0 + 6
Exercise 1.1.3 “11^2”
2^1 2^0
2 1
X X
1 1 2 + 1 = 3
Exercise 1.1.4 “10010^2”
2^4 2^3 2^2 2^1 2^0
16 8 4 2 1
X X X X X
1 0 0 1 0 16 + 2 = 18
Exercise 1.1.5 “11100010^2”
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
X X X X X X X X
1 1 1 0 0 0 1 0
128 + 64 + 32 + 2 = 226
Exercise 1.1.6 “156”
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
X X X X X X X X
1 0 0 1 1 1 0 0 128 + 16 + 8 + 4 = 156
Exercise 1.1.7 “255”
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
X X X X X X X X
1 1 1 1 1 1 1 1
128 + 64 + 32 + 1 6 + 8 + 4 + 2 + 1 = 255.
Exercise 1.1.8 “200”
2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
128 64 32 16 8 4 2 1
X X X X X X X X
1 1 0 0 1 0 0 0 128 + 68 + 8 = 200
Exercise 1.1.9 “1001^2” Exercise 1.1.10 “10111001^2” 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 128 64 32 16 8 4 2 1
Binary 1 0 1 1 1 0 0 1 128 0 32 16 8 0 0 1
Decimal 185

Exercise 1.1.11 “101111^2” Exercise 1.1.12 “10000001^2” 1.1 REVIEW
1) I started with 127 and 27(128). You can’t subtract 128 from 127 so I put a zero and moved on to 26(64). You can subtract 64 from 127, so I put down a 1 and the remainder is 63. I then use 63 and move on to 25(32). You can subtract 32from 63 so I put down a zero and the remainder is 31. I use 31 and move onto 24(16). You can subtract 16 from 31, put down a 1 and have a remainder of 15. Use15 move onto 23(8). You can subtract 8 from 15, put down a 1 remainder 7. Use7 and 22(4). You can subtract 4 from 7, put down a 1 remainder 3. Now use 3and 21(2). You can subtract 2 from 3, put down a zero remainder 1. Use 1 and 20(1). You can subtract 1 from 1. Put down a 1 and it’s complete. Binary number is 011111112
2) Zeros to the left don’t count they are sort of just like place holders so 10 is the same as 0010.
3) Available digit values would be 0,1,2,3,4. The first four digit would be 1, 5, 25,and 125.
4) Creating a converter from decimal to binary is more difficult because it requires more steps and more equations. You would have to formulate an equation that decided if the decimal digit is larger than the countdown. Then you would have to find a formula that would do the subtraction and now use that countdown.