CS273

Homework 1 Solution

For all the problems that involve conversions to and from decimal, use the multiplication method to convert to decimal, and the division method to convert from decimal.

From the Book

from page 45 and 46

1-2 (8 points)
- (b) 37 _Hex = ___________₂
```
   3         7   (hex)
 0011      0111  (binary)
```
  answer: 00110111₂
- (e) 99 _Hex = _____________₁₀
  
  Old Digit New Radix
  
  0 9 9 16
  
  144 9 153
  
  answer: 153₁₀
- (f) 10000011₂ = _______________₈
```
  2   0   3   (oct)
 010 000 011  (binary)
```
  answer: 203₈
- (g) 57₈ = _______________₁₀
  
  Old Digit New Radix
  
  0 5 5 8
  
  40 7 47
  
  answer: 47₁₀
1-4 (10 points) Due to no lecture on material - extra credit
- (a) 00000001
  
  Old Digit New Radix
  
  0 1 1
  
  answer: +1₁₀
- (c) 0000000000111111
  
  Old Digit New Radix
  
  0 1 1 2
  
  2 1 3 2
  
  6 1 7 2
  
  14 1 15 2
  
  30 1 31 2
  
  62 1 63
  
  answer: +63₁₀
- (d) 00000000
  answer: 0₁₀
- (f) 01111111
  
  Old Digit New Radix
  
  0 1 1 2
  
  2 1 3 2
  
  6 1 7 2
  
  14 1 15 2
  
  30 1 31 2
  
  62 1 63 2
  
  126 1 127
  
  answer: +127₁₀
- (i) 01000000
  
  Old Digit New Radix
  
  0 1 1 2
  
  2 0 2 2
  
  4 0 4 2
  
  8 0 8 2
  
  16 0 16 2
  
  32 0 32 2
  
  64 0 64
  
  answer: +64₁₀

1-5 (10 points)

(b) 10110101

 
 1011      0101  (binary)
   b         5   (hex)

answer: b5₁₆

(c) 00111101

 
 0011      1101  (binary)
   3         d   (hex)

answer: 3d₁₆

(e) 1010101101101100

 
 1010      1011      0110      1100  (binary)
   a         b         6         c   (hex)

answer: ab6c₁₆

(h) 01100111

 
 0110      0111  (binary)
   6         7   (hex)

answer: 67₁₆

(j) 0110111011101111

 
 0110      1110      1110      1111  (binary)
   6         e         e         f   (hex)

answer: 6eef₁₆

1-8 (2 points)

answer: 11001101₂

Not From the Book

(2 points) Convert from 654₁₀ to radix base 7.

Old Radix New Digit

654 7 93 3

93 7 13 2

13 7 1 6

1 7 0 1

Answer: 1623₇

(4 points) Convert from 5fc₁₆ to radix base 9.

Old	Digit	New	Radix
0	5	5	16
80	f(15₁₀)	95	16
1520	c(12₁₀)	1532

sub answer: 1532₁₀

Old	Radix	New	Digit
1532	9	170	2
170	9	18	8
18	9	2	0
2	9	0	2

Answer: 2082₉

(4 points) Using the algebric method discover the value of r given that 8_r * 9_r = 44_r
```
8₁₀ * 9₁₀ = 72₁₀

4*r + 4 = 72
    4*r = 68
	  r = 17
	
```
(10 points) Using your Lab1 program, change the program to use the A accumulator instructions and then answer the following questions using the simulator:
- Using your listing file, what opcode is shown for the instruction performing loading (line 2)?
  answer: 86
- Using you listing file, what opcode is shown for the instructions performing adding (line 3)?
  answer: 8b
- What is in the A and B accumulators on cycle 0? (Note: no steps have been executed in the simulator.)
  answer: A - 00, B - 00
- What is in the A and B accumulators on cycle 2?
  answer: A - 24, B - 00
- What is in the A and B accumulators on cycle 7?
  answer: A - 36, B - 00
- What is in the PC on cycle 7?
  answer: PC - F804
- What is the opcode for the ``bra'' instruction?
  answer: 20

Last modified: Sat Sep 11 22:18:29 MDT 2001