Summary

1And in Summary$\dots$¶

• We represent “things” in computers as particular bit patterns:

  • With N bits, you can represent at most 2N things.

• Today, we discussed five different encodings for integers:

  • Unsigned integers

  • Signed integers:

  • Sign-Magnitude

  • Ones’ Complement

  • Two’s Complement

  • Bias Encoding

• Computer architects make design decisions to make HW simple

  • Unsigned and Two’s complement are C standard. Learn them!!

• Integer overflow: The result of an arithmetic operation is outside the representable range of integers.

  • Numbers have infinite digits, but computers have finite precision. This can lead to arithmetic errors. More later!

Meta takeaway: We make design decisions to make the hardware simple. We threw out sign magnitude and ones’ complement because the hardware would be hard. But here’s a secret: it’s the same hardware for mathematics on unsigned and two’s complement numbers. The only difference is how you calculate overflow.

2Textbook readings¶

P&H: 2.4

3Additional Reading¶

Dan Garcia’s Binary Slides, Fall 2025

Amazing Illustrations by Ketrina (Yim) Thompson: CS Illustrated Number Rep Handouts

• Comparing Binary Integer Representations

• Negation and Zeroes

• Increments and Monotonicity

• The Thrilling Conclusion!