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Problems 297
P6.24 MATLAB provides the built-in functions dec2bin and bin2dec to convert non-negative
decimal integers into binary codes and vice versa, respectively.
1. Develop a function B = sm2bin(D) to convert a sign-magnitude format decimal integer D
into its binary representation B. Verify your function on the following numbers:
(a) D = 1001 (b) D = −63 (c) D = −449 (d) D = 978 (e) D = −205
2. Develop a function D = bin2sm(B) to convert a binary representation B into its signmagnitude
format decimal integer D. Verify your function on the following
representations:
(a) B = 1010 (b) B = 011011011 (c) B = 11001
(d) B = 1010101 (e) B = 011011
P6.25 Using the function TwosComplement as a model, develop a function y = TensComplement
(x,N) that converts a sign-magnitude format integer x into the N-digit ten’s-complement
integer y.
1. Verify your function using the following integers:
(a) x = 1234, N=6 (b) x = −603, N=4 (c) x = −843, N=5
(d) x = −1978, N=6
(e) x =50,N=3
2. Using the ten’s-complement format, perform the following arithmetic operations. In each
case, choose an appropriate value on N for the meaningful result.
(a) 123 + 456 − 789 (b) 648 + 836 − 452 (c) 2001 + 3756
(d) −968 + 4539 (e) 888 − 666 + 777
Verify your results using decimal operations.
P6.26 The function OnesComplement developed in this chapter converts signed integers into one’scomplement
format decimal representations. In this problem we will develop functions that
will operate on fractional numbers.
1. Develop a MATLAB function y = sm2oc(x, B) that converts the sign-magnitude format
fraction x into the B-bit 1s-complement format decimal equivalent number y. Verify
your function on the following numbers. In each case the numbers to be considered are
both positive and negative. Also, in each case select the appropriate number of bits B.
(a) x = ±0.5625 (b) x = ±0.40625 (c) x = ±0.953125
(d) x = ±0.1328125 (e) x = ±0.7314453125
2. Develop a MATLAB function x = oc2sm(y, B) that converts the B-bit one’s-complement
format decimal equivalent number y into the sign-magnitude format fraction x. Verify
your function on the following fractional binary representations:
(a) y = 110110 (b) y = 0.011001 (c) y = 100110011
(d) y = 111101110
(e) y = 000010001
P6.27 The function TwosComplement developed in this chapter converts signed integers into two’scomplement
format decimal representations. In this problem we will develop functions that
will operate on fractional numbers.
1. Develop a MATLAB function y = sm2tc(x, B) that converts the sign-magnitude format
fraction x into the B-bit two’s-complement format decimal equivalent number y. Verify
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