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[Page 1245]

D.1

10, 2, 8, 16.

D.2

Fewer.

D.3

D.4

D.5

False. The highest digit in any base is one less than the base.

D.6

False. The lowest digit in any base is zero.

D.7

1 (the base raised to the zero power).

D.8

The base of the number system.

D.9

Fill in the missing values in this chart of positional values for the rightmost four positions in each of the indicated number systems:

 decimal 1000 100 10 1 hexadecimal 4096 256 16 1 binary 8 4 2 1 octal 512 64 8 1

D.10

D.11

Binary 1111 1010 1100 1110.

D.12

Binary 111 011 001 110.

D.13

Binary 0 100 111 111 101 100; Octal 47754.

D.14

Decimal 2+4+8+32+64=110.

D.15

Decimal 7+1*8+3*64=7+8+192=207.

D.16

Decimal 4+13*16+15*256+14*4096=61396.

D.17

Decimal 177

to binary:

```256 128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1
(1*128)+(0*64)+(1*32)+(1*16)+(0*8)+(0*4)+(0*2)+(1*1)
10110001
```

to octal:

```512 64 8 1
64 8 1
(2*64)+(6*8)+(1*1)
261
```

```256 16 1
16 1
(11*16)+(1*1)
(B*16)+(1*1)
B1
```

D.18

Binary:

```[Page 1246]512 256 128 64 32 16 8 4 2 1
256 128 64 32 16 8 4 2 1
(1*256)+(1*128)+(0*64)+(1*32)+(0*16)+(0*8)+(0*4)+(0*2)+(1*1)
110100001
```

One's complement: 001011110

Two's complement: 001011111

Check: Original binary number + its two's complement

```110100001
001011111
---------
000000000
```

D.19

Zero.