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 2.17PP
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)i=0w1xi2i

  • 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” contain 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

Two’s-Complement encodings:

  • The two’s complement encoding is represented by the interpretation function of “B2Tw”.
    • The function “B2Tw” means “binary to two’s-complement” of length “w”.
  • The equation for “B2Tw” is

    B2Tw(x)xw12w1+i=0w2xi2i

  • From the above equation,
    • The notation denotes that the side of left-hand is defined to be equal to the side of right-hand.
    • “xw-1” is the most significant bit. It is also named as “sign bit”.
      • It weight “-2w-1” means the weight is in negation for representation of an unsigned.
        • When the sign bit is set to “1”, then the value is denoted by “negative”.
        • When the sign bit is set to “0”, then the value is denoted by “nonnegative”.
    • The bit length is “w”.
    • A bit vector is x  which is denoted by entire vector or [xw1,xw2,........,x0]:
    • Each bit “xi” contain value “0” or “1”.

Example:

The example of “B2Tw” is shown below:

Consider, value of x is “1111” which contains bits length “4”.

Therefore using the above equation, user can compute the B2T4(1111)

B2T4(1111)=-1×23+1×22+1×21+1×20 =-1×8+1×4+1×2+1×1 =-8+4+2+1 =-1

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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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