P2

a. $2^{10}=32,768$

b. $64*2^{20}=67,108,864$

c. $6.4*2^{30}=6,871,947,674$

P3

$2^{12} - 1 = 4095 = (111111111111)_{12} = (FFF)_{16} = (7777)_{8}$

P4

$(4310)_5 = 0 + 1X5 + 3X5^2 + 4X5^3 = (580)_{10}$

$(198)_{12} = 8 + 9X12 + 1X12^2 = (260)_{10}$

P6

$x^2 - 11x - 22 = 0 ; x=3,x=6$

Convert all numbers to decimal from Base "N":

$x^2 - (N+1)x - (2N+2) = 0 ; x=3,x=6$

Insert x=3:

$3^2 - (N+1)3 - (2N+2) = 0$

$N = 8$

Check with x=6:

$6^2 - (N+1)6 - (2N+2) = 0$

$4N = 32$

$N = 8$

P7

Convert to decimal:

$10110.0101 = 2 + 4 + 16 + 1/4 + 1/16 = 22 \frac{5}{16} = 22.31$

$(16.5)_{16} = 6 + 16 + 5/16 = 22 \frac{5}{16} = 22.31$

$(26.24)_{8} = 6 + 2*8 + 2/8 + 4/64 = 22 \frac{5}{16} = 22.31$

P7

Convert 68BE to octal through binary:

$\overbrace{ \underbrace{0}_0 \underbrace{110}_6 }^6 \overbrace{ \underbrace{01... ...brace{\underbrace{10}_211}^B \overbrace{\underbrace{1}_7 \underbrace{110}_6}^E$

P12

$\begin{array}{rrrr} & Add & & Mult \\ & 1011 & & 1011 \\ + & \underline{10... ..._{16} & & B8 \\ & & & \underline{8A0} \\ & & & (958)_{16} \\ \end{array}$

P14

$\begin{array}{ccc} Number & 9s comp & 10s comp \\ 98127634 & 01872365 & 0187... ...00 & 89999999 & 90000000 \\ 00000000 & 99999999 & 100000000 \\ \end{array}$

P16

$\begin{array}{ccc} Number & 1s comp & 2s comp \\ 11101010 & 00010101 & 00010... ...00 & 01111111 & 10000000 \\ 00000000 & 11111111 & 100000000 \\ \end{array}$

P17

$\begin{array}{rrrrrrrr} & 7188 & & 0150 & & 2997 & & 1321 \\ +& \underline{6... ...boxed{0}5005 & & \boxed{1}0946 \\ & & & -1950 & & -4995 & & \\ \end{array}$

P18

$\begin{array}{rrrrrrrr} & 11011 & & 110100 & & 001011 & & 101010 \\ +& \unde... ...}011011 & & \boxed{0}111111 \\ & & & & & -100101 & &-000001 \\ \end{array}$

P20

Convert +61 and +27 to binary using the signe 2's complement representation and enough digits to accomodate the numbers, then perform the binary equivalent of: 27 + (-61); (-27) + 61 ; (-27) + (-61).

$\begin{array}{crcrcrcrcrcr} & +27 & & 00011011 & & -27 & & 11100101 & & -27 & ... ...11110 & & +34 & & \boxed{1}00100010 & & -88 & & \boxed{1}10101000 \end{array}$

Discard the boxed end carries above.

P32a,d

The state of a 12 bit register is 100010010111 What is it's contents in:

a) BCD - 897

d) Binary - 2199

P33

List the ASCII code for the 10 decimal digits with an even parity bit in the leftmost position:

$\begin{array}{cc} 0 & \underbar{0}0110000 \\ 1 & \underbar{1}0110001 \\ 2 ... ...\\ 8 & \underbar{1}0111000 \\ 9 & \underbar{0}0111001 \\ \par\end{array}$

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ECE 201; HW solutions for 3rd Edition; Chapter 1

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