Computer Systems: A Programmer's Perspective (3rd Edition)
Computer Systems: A Programmer's Perspective (3rd Edition)
3rd Edition
ISBN: 9780134092669
Author: Bryant, Randal E. Bryant, David R. O'Hallaron, David R., Randal E.; O'Hallaron, Bryant/O'hallaron
Publisher: PEARSON
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Chapter 2.2, Problem 2.19PP
Program Plan Intro

Unsigned encoding:

  • The unsigned encoding is represented by the interpretation function of “B2Uw”.
    • The function “B2Uw” means “binary to unsigned” of length “w”.
  • The equation for “B2Uw” is

    B2Uw(x)Bi=0w-1xi2i

  • From the above equation,
    • The notation denotes that the side of left-hand is defined to be equal to the side of right-hand.
    • The function “B2Uw” maps string of 0’s and 1’s of length “w” to nonnegative integers.
    • The bit length is “w”.
    • A bit vector is x  which is denoted by entire vector or [xw1,xw2,........,x0]:
    • Each bit “xi” contains value “0” or “1”.

Example:

The example of “B2Uw” is shown below:

Consider, value of x is “0100” which contains bits length “4”.

Therefore using the above equation, user can compute the B2U4(0100)

B2U4(0100)=0×23+1×22+0×21+0×20 =0+4+0+0 =4

“T2U” function:

  • The function “T2U” means conversion of “Two’s complement to unsigned” with “w” length bits.
  • This function is computed by the below formula

    T2Uw(x)=B2Uw(T2Bw(x))

  • From the above equation, first convert the two’s complement to binary and then convert the binary to unsigned.

Example:

The example of “T2Uw” is shown below:

Consider, value of x is “-6” and bit length is “4”.

To find the two’s complement, first need to take 1’s complement to given binary and then add one with it.

The formula for find the value of “T2Uw” is given below

T2U4(-6)=B2U4(T2B4(-6))

Step 1: convert the two’s complement to binary

Binary value of “6”: 0110

1’s complement of “0110”: 1001

Add 1:       1

---------------------------------------------

2’s complement of binary: 1010 (-6)

Therefore, T2B4(6)=1010

Step 2: convert the given binary to unsigned.

B2U4(1010)=1×23+0×22+1×21+0×20 =1×8+0+1×2+0 =8+0+2+0 =10

T2U4(-6)=B2U4(1010)=10

Therefore, T2U4(-6)=10

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Chapter 2 Solutions

Computer Systems: A Programmer's Perspective (3rd Edition)

Ch. 2.1 - Prob. 2.11PPCh. 2.1 - Prob. 2.12PPCh. 2.1 - Prob. 2.13PPCh. 2.1 - Prob. 2.14PPCh. 2.1 - Prob. 2.15PPCh. 2.1 - Prob. 2.16PPCh. 2.2 - Prob. 2.17PPCh. 2.2 - Practice Problem 2.18 (solution page 149) In...Ch. 2.2 - Prob. 2.19PPCh. 2.2 - Prob. 2.20PPCh. 2.2 - Prob. 2.21PPCh. 2.2 - Prob. 2.22PPCh. 2.2 - Prob. 2.23PPCh. 2.2 - Prob. 2.24PPCh. 2.2 - Prob. 2.25PPCh. 2.2 - Practice Problem 2.26 (solution page 151) You are...Ch. 2.3 - Prob. 2.27PPCh. 2.3 - Prob. 2.28PPCh. 2.3 - Prob. 2.29PPCh. 2.3 - Practice Problem 2.30 (solution page 153) Write a...Ch. 2.3 - Prob. 2.31PPCh. 2.3 - Practice Problem 2.32 (solution page 153) You are...Ch. 2.3 - Prob. 2.33PPCh. 2.3 - Prob. 2.34PPCh. 2.3 - Practice Problem 2.35 (solution page 154) You are...Ch. 2.3 - Prob. 2.36PPCh. 2.3 - Practice Problem 2.37 solution page 155 You are...Ch. 2.3 - Prob. 2.38PPCh. 2.3 - Prob. 2.39PPCh. 2.3 - Practice Problem 2.40 (solution page 156) For each...Ch. 2.3 - Prob. 2.41PPCh. 2.3 - Practice Problem 2.42 (solution page 156) Write a...Ch. 2.3 - Practice Problem 2.43 (solution page 157) In the...Ch. 2.3 - Prob. 2.44PPCh. 2.4 - Prob. 2.45PPCh. 2.4 - Prob. 2.46PPCh. 2.4 - Prob. 2.47PPCh. 2.4 - Prob. 2.48PPCh. 2.4 - Prob. 2.49PPCh. 2.4 - Prob. 2.50PPCh. 2.4 - Prob. 2.51PPCh. 2.4 - Prob. 2.52PPCh. 2.4 - Practice Problem 2.53 (solution page 160) Fill in...Ch. 2.4 - Practice Problem 2.54 (solution page 160) Assume...Ch. 2 - Compile and run the sample code that uses...Ch. 2 - Try running the code for show_bytes for different...Ch. 2 - Prob. 2.57HWCh. 2 - Write a procedure is_little_endian that will...Ch. 2 - Prob. 2.59HWCh. 2 - Prob. 2.60HWCh. 2 - Prob. 2.61HWCh. 2 - Write a function int_shifts_are_arithmetic() that...Ch. 2 - Fill in code for the following C functions....Ch. 2 - Write code to implement the following function: /...Ch. 2 - Write code to implement the following function: /...Ch. 2 - Write code to implement the following function: / ...Ch. 2 - You are given the task of writing a procedure...Ch. 2 - Prob. 2.68HWCh. 2 - Write code for a function with the following...Ch. 2 - Write code for the function with the following...Ch. 2 - You just started working for a company that is...Ch. 2 - You are given the task of writing a function that...Ch. 2 - Write code for a function with the following...Ch. 2 - Write a function with the following prototype: /...Ch. 2 - Prob. 2.75HWCh. 2 - The library function calloc has the following...Ch. 2 - Prob. 2.77HWCh. 2 - Write code for a function with the following...Ch. 2 - Prob. 2.79HWCh. 2 - Write code for a function threefourths that, for...Ch. 2 - Prob. 2.81HWCh. 2 - Prob. 2.82HWCh. 2 - Prob. 2.83HWCh. 2 - Prob. 2.84HWCh. 2 - Prob. 2.85HWCh. 2 - Intel-compatible processors also support an...Ch. 2 - Prob. 2.87HWCh. 2 - Prob. 2.88HWCh. 2 - We are running programs on a machine where values...Ch. 2 - You have been assigned the task of writing a C...Ch. 2 - Prob. 2.91HWCh. 2 - Prob. 2.92HWCh. 2 - following the bit-level floating-point coding...Ch. 2 - Following the bit-level floating-point coding...Ch. 2 - Following the bit-level floating-point coding...Ch. 2 - Following the bit-level floating-point coding...Ch. 2 - Prob. 2.97HW
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