Erik Jonsson School of Engineering and Computer Science FEARLESS Engineeringwww.utdallas.edu/~pervin EE/CE 2310 – HON/002 Introduction to Digital Systems Tuesday: Review for Examination II Thursday

EXAMINATION II: 5 A PRIL 2012 (P) 5 Functions and Stacks 6 File and Character IO 7 Recursion (T) 8 Arithmetic 9 Flip-Flops (1-6) 10 Counters (1-4) 11 Shifts (1-3)

Serial-Load Shift Reg.

Parallel-Load Shift Reg.

C(n,k) = C(n-1,k) + C(n-1,k-1); Pascal Triangle

C(n,k) = C(n-1,k) + C(n-1,k-1); Order

P ASCAL T RIANGLE

Dynamic Programming

T IMING D IAGRAM

F = AC’D + BC + A’C

TIMING

EXAMINATION II: 5 April 2012 (P) 5 Functions and Stacks 6 File and Character IO 7 Recursion (T) 8 Arithmetic 9 Flip-Flops (1-6) 10 Counters (1-4) 11 Shifts (1-3)

Floating-Point Numbers IEEE Standard Our text only refers to the very similar IEEE Standard

Normalized Numbers: Decisions: Base, Sign, Exponent, Mantissa

Decisions: (32-bit words) Base: 2 Sign: Bit 31 (0 = pos, 1 = neg) Exponent: 8 bits (biased by -127 ; not 2’s complement or other) Mantissa: 23 remaining bits (with 1. understood to give 24 bit accuracy)

Decisions: (64-bit words) “double” Base: 2 Sign: Bit 31 of the first word (0 = pos, 1 = neg) Exponent: 11 bits (biased by ; not 2’s complement or other) Mantissa: 20+32=52 remaining bits (with 1. understood to give 33 bit accuracy)

Decisions: (128-bit words) “quad” Base: 2 Sign: Bit 31 of the first word (0 = pos, 1 = neg) Exponent: 15 bits (biased by ; not 2’s complement or other) Mantissa: 112 remaining bits (with 1. understood to give 33 bit accuracy)

Special Cases: Zero Denormalized numbers Positive and negative infinity NaN Some other decisions:

We cannot store the important number 1/10 exactly in a binary computer!