COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG
COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG
3rd Edition
ISBN: 9780134671123
Author: Bryant
Publisher: PEARSON
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Chapter 2.3, Problem 2.33PP
Program Plan Intro

Two’s complement negation:

The two’s-complement negation is represented by “-wt

For any number “x” such that TMinw  x  TMaxw, its “w-bit” two’s-complement negation is denoted by below formula 

-wtx = {TMinw,           x = TMinw- x,   x > TMinw}

From the above equation, “TMinw” is its own additive inverse, though any other value “x” has “-x” as its additive inverse.

  • When “x” is “TMinw”, then its two’s-complement negation value is “TMinw”.
  • When “x > TMinw”, then its two’s-complement negation value is “–x”.

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)=B-xw-12w-1+i=0w-2xi2i

Example:

The example for two’s-complement negation is shown below:

Here assume bit length, “w” is “4” and “TMin4” is “-8”.

Case 1: consider the value of “x” is “0”, then -4t0 = 0.

Case 2: consider the value of “x” is “6”

Step 1: compute the decimal value for given hex value

  • The binary value for “0x6” is “0110”.
  • Compute the B2T4(0110) by using the above equation of “B2Tw

    B2T4(0110)=-0×23+1×22+1×21+0×20 =-0+4+2+0 =6

B2T4(0110)=6

Therefore, decimal value for given hex value is “6”.

Step 2: compute the two’s-complement of decimal and hex value from step 1

Here, the decimal value of “x” from step 1 is “6” then check condition “x > TMinw” that is “6 > -8”. So, compute the two’s-complement negation by using -wtx = - x

-4t= -6      = -6

Therefore, the decimal value is “-6”. Here the value is in negative. So, need to compute two’s-complements.

Binary value for “6”: 0110

1’s complement: 1001

Add 1:       1

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

2’s complement: 1010 (A)

Therefore, the corresponding hex value for “-6” is “A”.

Table for corresponding hexadecimal and binary value:

Hex digit01234567
Decimal value01234567
Hex digit89ABCDEF
Decimal value89101112131415

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Chapter 2 Solutions

COMPUTER SYSTEMS&MOD MSGT/ET SA AC PKG

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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